This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
Today,with the rapid development of the internet,a large amount of information often accompanies the rapid transmission of disease outbreaks,and increasing numbers of scholars are studying the relationship between inf...Today,with the rapid development of the internet,a large amount of information often accompanies the rapid transmission of disease outbreaks,and increasing numbers of scholars are studying the relationship between information and the disease transmission process using complex networks.In fact,the disease transmission process is very complex.Besides this information,there will often be individual behavioral measures and other factors to consider.Most of the previous research has aimed to establish a two-layer network model to consider the impact of information on the transmission process of disease,rarely divided into information and behavior,respectively.To carry out a more in-depth analysis of the disease transmission process and the intrinsic influencing mechanism,this paper divides information and behavior into two layers and proposes the establishment of a complex network to study the dynamic co-evolution of information diffusion,vaccination behavior,and disease transmission.This is achieved by considering four influential relationships between adjacent layers in multilayer networks.In the information layer,the diffusion process of negative information is described,and the feedback effects of local and global vaccination are considered.In the behavioral layer,an individual's vaccination behavior is described,and the probability of an individual receiving a vaccination is influenced by two factors:the influence of negative information,and the influence of local and global disease severity.In the disease layer,individual susceptibility is considered to be influenced by vaccination behavior.The state transition equations are derived using the micro Markov chain approach(MMCA),and disease prevalence thresholds are obtained.It is demonstrated through simulation experiments that the negative information diffusion is less influenced by local vaccination behavior,and is mainly influenced by global vaccination behavior;vaccination behavior is mainly influenced by local disease conditions,and is less influenced by global disease conditions;the disease transmission threshold increases with the increasing vaccination rate;and the scale of disease transmission increases with the increasing negative information diffusion rate and decreases with the increasing vaccination rate.Finally,it is found that when individual vaccination behavior considers both the influence of negative information and disease,it can increase the disease transmission threshold and reduce the scale of disease transmission.Therefore,we should resist the diffusion of negative information,increase vaccination proportions,and take appropriate protective measures in time.展开更多
Pose-invariant facial expression recognition(FER)is an active but challenging research topic in computer vision.Especially with the involvement of diverse observation angles,FER makes the training parameter models inc...Pose-invariant facial expression recognition(FER)is an active but challenging research topic in computer vision.Especially with the involvement of diverse observation angles,FER makes the training parameter models inconsistent from one view to another.This study develops a deep global multiple-scale and local patches attention(GMS-LPA)dual-branch network for pose-invariant FER to weaken the influence of pose variation and selfocclusion on recognition accuracy.In this research,the designed GMS-LPA network contains four main parts,i.e.,the feature extraction module,the global multiple-scale(GMS)module,the local patches attention(LPA)module,and the model-level fusion model.The feature extraction module is designed to extract and normalize texture information to the same size.The GMS model can extract deep global features with different receptive fields,releasing the sensitivity of deeper convolution layers to pose-variant and self-occlusion.The LPA module is built to force the network to focus on local salient features,which can lower the effect of pose variation and self-occlusion on recognition results.Subsequently,the extracted features are fused with a model-level strategy to improve recognition accuracy.Extensive experimentswere conducted on four public databases,and the recognition results demonstrated the feasibility and validity of the proposed methods.展开更多
Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting app...Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-obj...Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.展开更多
In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the glob...In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.展开更多
Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of ...Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of the existing node centrality measure only considering the specific statistical feature of a single dimension, a SLGC model is proposed that combines a node’s self-influence, its local neighborhood influence, and global influence to identify influential nodes in the network. The exponential function of e is introduced to measure the node’s self-influence;in the local neighborhood,the node’s one-hop neighboring nodes and two-hop neighboring nodes are considered, while the information entropy is introduced to measure the node’s local influence;the topological position of the node in the network and the shortest path between nodes are considered to measure the node’s global influence. To demonstrate the effectiveness of the proposed model, extensive comparison experiments are conducted with eight existing node centrality measures on six real network data sets using node differentiation ability experiments, susceptible–infected–recovered(SIR) model and network efficiency as evaluation criteria. The experimental results show that the method can identify influential nodes in complex networks more accurately.展开更多
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
The authors prove the local existence and uniqueness of weak solution of a hyperbolic-parabolic system and establish the global existence of the weak solution for this system for the spatial dimension n = 1.
In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local exist...In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.展开更多
This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifur...This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu (Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350(12), 4799-4838 (1998)).展开更多
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result o...By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.展开更多
This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l + u^p1v^q1 and vt = △v ^m + u^p2 v^q2 with homogeneous Dirichlet boundary conditions....This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l + u^p1v^q1 and vt = △v ^m + u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - (l -p1)(m- q2), the initial data, and the domain Ω.展开更多
In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potentia...In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E(0) 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E(0) 〈 0.展开更多
We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical s...We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.展开更多
In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equatio...In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.展开更多
In this paper, we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation. Moreover, we show that the supremum norm of the solution decays algebraically...In this paper, we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation. Moreover, we show that the supremum norm of the solution decays algebraically to zero as (1 + t)-(1/7) when t approaches to infinity, provided the initial data are sufficiently small and regular.展开更多
In this paper we consider the Elastic membrane equation:with memory term and nonlinear boundary damping: Under some appropriate assumptions on the relaxation function h and with certain initial data, the global exis...In this paper we consider the Elastic membrane equation:with memory term and nonlinear boundary damping: Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions :and a general decay for the energy are established using the multiplier technique. Also, 'we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping.展开更多
This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multipli...This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.展开更多
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 72174121 and 71774111)the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learningthe Natural Science Foundation of Shanghai (Grant No. 21ZR1444100)
文摘Today,with the rapid development of the internet,a large amount of information often accompanies the rapid transmission of disease outbreaks,and increasing numbers of scholars are studying the relationship between information and the disease transmission process using complex networks.In fact,the disease transmission process is very complex.Besides this information,there will often be individual behavioral measures and other factors to consider.Most of the previous research has aimed to establish a two-layer network model to consider the impact of information on the transmission process of disease,rarely divided into information and behavior,respectively.To carry out a more in-depth analysis of the disease transmission process and the intrinsic influencing mechanism,this paper divides information and behavior into two layers and proposes the establishment of a complex network to study the dynamic co-evolution of information diffusion,vaccination behavior,and disease transmission.This is achieved by considering four influential relationships between adjacent layers in multilayer networks.In the information layer,the diffusion process of negative information is described,and the feedback effects of local and global vaccination are considered.In the behavioral layer,an individual's vaccination behavior is described,and the probability of an individual receiving a vaccination is influenced by two factors:the influence of negative information,and the influence of local and global disease severity.In the disease layer,individual susceptibility is considered to be influenced by vaccination behavior.The state transition equations are derived using the micro Markov chain approach(MMCA),and disease prevalence thresholds are obtained.It is demonstrated through simulation experiments that the negative information diffusion is less influenced by local vaccination behavior,and is mainly influenced by global vaccination behavior;vaccination behavior is mainly influenced by local disease conditions,and is less influenced by global disease conditions;the disease transmission threshold increases with the increasing vaccination rate;and the scale of disease transmission increases with the increasing negative information diffusion rate and decreases with the increasing vaccination rate.Finally,it is found that when individual vaccination behavior considers both the influence of negative information and disease,it can increase the disease transmission threshold and reduce the scale of disease transmission.Therefore,we should resist the diffusion of negative information,increase vaccination proportions,and take appropriate protective measures in time.
基金supported by the National Natural Science Foundation of China (No.31872399)Advantage Discipline Construction Project (PAPD,No.6-2018)of Jiangsu University。
文摘Pose-invariant facial expression recognition(FER)is an active but challenging research topic in computer vision.Especially with the involvement of diverse observation angles,FER makes the training parameter models inconsistent from one view to another.This study develops a deep global multiple-scale and local patches attention(GMS-LPA)dual-branch network for pose-invariant FER to weaken the influence of pose variation and selfocclusion on recognition accuracy.In this research,the designed GMS-LPA network contains four main parts,i.e.,the feature extraction module,the global multiple-scale(GMS)module,the local patches attention(LPA)module,and the model-level fusion model.The feature extraction module is designed to extract and normalize texture information to the same size.The GMS model can extract deep global features with different receptive fields,releasing the sensitivity of deeper convolution layers to pose-variant and self-occlusion.The LPA module is built to force the network to focus on local salient features,which can lower the effect of pose variation and self-occlusion on recognition results.Subsequently,the extracted features are fused with a model-level strategy to improve recognition accuracy.Extensive experimentswere conducted on four public databases,and the recognition results demonstrated the feasibility and validity of the proposed methods.
基金Project supported by the National Natural Science Foundation of China(Nos.11932008 and 12272156)the Fundamental Research Funds for the Central Universities(No.lzujbky-2022-kb06)+1 种基金the Gansu Science and Technology ProgramLanzhou City’s Scientific Research Funding Subsidy to Lanzhou University of China。
文摘Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
基金supported in part by the National Natural Science Fund for Outstanding Young Scholars of China (61922072)the National Natural Science Foundation of China (62176238, 61806179, 61876169, 61976237)+2 种基金China Postdoctoral Science Foundation (2020M682347)the Training Program of Young Backbone Teachers in Colleges and Universities in Henan Province (2020GGJS006)Henan Provincial Young Talents Lifting Project (2021HYTP007)。
文摘Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.
文摘In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.
基金Project supported by the Natural Science Basic Research Program of Shaanxi Province of China (Grant No. 2022JQ675)the Youth Innovation Team of Shaanxi Universities。
文摘Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of the existing node centrality measure only considering the specific statistical feature of a single dimension, a SLGC model is proposed that combines a node’s self-influence, its local neighborhood influence, and global influence to identify influential nodes in the network. The exponential function of e is introduced to measure the node’s self-influence;in the local neighborhood,the node’s one-hop neighboring nodes and two-hop neighboring nodes are considered, while the information entropy is introduced to measure the node’s local influence;the topological position of the node in the network and the shortest path between nodes are considered to measure the node’s global influence. To demonstrate the effectiveness of the proposed model, extensive comparison experiments are conducted with eight existing node centrality measures on six real network data sets using node differentiation ability experiments, susceptible–infected–recovered(SIR) model and network efficiency as evaluation criteria. The experimental results show that the method can identify influential nodes in complex networks more accurately.
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
文摘The authors prove the local existence and uniqueness of weak solution of a hyperbolic-parabolic system and establish the global existence of the weak solution for this system for the spatial dimension n = 1.
基金supported by a grant from the National High Technology Researchand and Development Program of China (863 Program) (2009AA044501)by NSFC (10776035+2 种基金10771085)by Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Educationby the 985 program of Jilin University
文摘In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.
基金Project supported by the National Natural Science Foundation of China (Nos. 10771215 and10771094)
文摘This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu (Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350(12), 4799-4838 (1998)).
文摘By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.
基金This work is supported in part by NNSF of China (10571126)in part by Program for New Century Excellent Talents in University.
文摘This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l + u^p1v^q1 and vt = △v ^m + u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - (l -p1)(m- q2), the initial data, and the domain Ω.
文摘In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E(0) 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E(0) 〈 0.
基金supported by the National Natural Science Foundation of China(11301172,11226170)China Postdoctoral Science Foundation funded project(2012M511640)Hunan Provincial Natural Science Foundation of China(13JJ4095)
文摘We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
文摘In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.
文摘In this paper, we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation. Moreover, we show that the supremum norm of the solution decays algebraically to zero as (1 + t)-(1/7) when t approaches to infinity, provided the initial data are sufficiently small and regular.
文摘In this paper we consider the Elastic membrane equation:with memory term and nonlinear boundary damping: Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions :and a general decay for the energy are established using the multiplier technique. Also, 'we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping.
基金Sponsored by the NNSF of China(11031003,11271066,11326158)a grant of Shanghai Education Commission(13ZZ048)Chinese Universities Scientific Fund(CUSF-DH-D-2013068)
文摘This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.