This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ...This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.展开更多
The Paraconsistent Many-Valued Similarity (PMVS) method for multi-attribute decision making will be incomplete as a decision model if it is not extended to the realm of group decision-making. Therefore, in this articl...The Paraconsistent Many-Valued Similarity (PMVS) method for multi-attribute decision making will be incomplete as a decision model if it is not extended to the realm of group decision-making. Therefore, in this article, our primary objective is to show how the paraconsistent many-valued similarity method can be used to solve group decision-making problems involving choice making or ranking of a finite set of decision alternatives. Moreover, since weights are very important parameters in multi-attribute decision-making, we have introduced the Borda rule to calculate the weights of experts and that of every criterion under consideration. To demonstrate how the proposed method works, a numerical example on energy sources of an economy from the points of view of a group of experts is investigated. Further, we compare the results of this new approach with that of fuzzy TOPSIS group decision-making method to illustrate the robustness and effectiveness of the former.展开更多
In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Land...In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many "singular" times, at which the energy concentration occurs and the director field losses its second order derivatives.展开更多
In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {(t, x) | t ≥ 0, x ≥0} is considered. A suffic...In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {(t, x) | t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.展开更多
In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ((φ(ρ))xxφ′(ρ))x with φ(ρ) = ρα. The model co...In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ((φ(ρ))xxφ′(ρ))x with φ(ρ) = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] (α=1/2) to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.展开更多
A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, whi...A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.展开更多
The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C([0, ∞) × R) ∩ L~∞([0, ∞); H1(R)) under the condition that its initial value ...The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C([0, ∞) × R) ∩ L~∞([0, ∞); H1(R)) under the condition that its initial value belongs to the space H1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.展开更多
In this paper, we study the global existence of weak solutions for the Cauchy problem of the nonlinear hyperbolic system of three equations(1.1) with bounded initial data(1.2). When we fix the third variable s, the sy...In this paper, we study the global existence of weak solutions for the Cauchy problem of the nonlinear hyperbolic system of three equations(1.1) with bounded initial data(1.2). When we fix the third variable s, the system about the variables ρ and u is the classical isentropic gas dynamics in Eulerian coordinates with the pressure function P(ρ, s) = ese-1/ρ,which, in general, does not form a bounded invariant region. We introduce a variant of the viscosity argument, and construct the approximate solutions of(1.1) and(1.2) by adding the artificial viscosity to the Riemann invariants system(2.1). When the amplitude of the first two Riemann invariants(w1(x, 0), w2(x, 0)) of system(1.1) is small,(w1(x, 0), w2(x, 0)) are nondecreasing and the third Riemann invariant s(x, 0) is of the bounded total variation, we obtained the necessary estimates and the pointwise convergence of the viscosity solutions by the compensated compactness theory. This is an extension of the results in [1].展开更多
Global in time weak solutions to the α-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to α-model regularization f...Global in time weak solutions to the α-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to α-model regularization for the three dimension compressible EulerPoisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies γ >4/3.展开更多
This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the ...This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.展开更多
The global well-posedness of another class of initial-boundary value problem on two/three-dimensional incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. The existence of...The global well-posedness of another class of initial-boundary value problem on two/three-dimensional incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD-Boussinesq equation with the given pressure-velocity’s relation boundary condition for the fluid field,one generalized perfectly conducting boundary condition for the magnetic field and one density/temperature-velocity’s relation boundary condition for the density/temapture at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also proven.展开更多
In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin app...In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin approximation and weak compactness theory.展开更多
Weak global navigation satellite system(GNSS) signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS sign...Weak global navigation satellite system(GNSS) signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS signal acquisition method using re-scaling and adaptive stochastic resonance(SR). The adoption of classical SR is limited to low-frequency and periodic signals. Given that GNSS signal frequency is high and that the periodic feature of the GNSS signal is affected by the Doppler frequency shift, classical SR methods cannot be directly used to acquire GNSS signals. Therefore, the re-scaling technique is used in our study to expand its usage to high-frequency signals and adaptive control technique is used to gradually determine the Doppler shift effect in GNSS signal buried in strong noises. The effectiveness of our proposed method was verified by the simulations on GPS L1 signals. The simulation results indicate that the new algorithm based on SR can reach-181 d BW sensitivity with a very short data length of 1 ms.展开更多
The existence of global BV solutions for the Aw-Rascle system with linear damping is considered.In order to get approximate solutions we consider the system in Lagrangian coordinates,then by using the wave front track...The existence of global BV solutions for the Aw-Rascle system with linear damping is considered.In order to get approximate solutions we consider the system in Lagrangian coordinates,then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of[1]we get a sequence of approximate solutions.Finally we show the convergence of this approximate sequence to the weak entropic solution.展开更多
We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating s...We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating sequences generatedby the method of vanishing viscosity. The uniqueness of the generalized solutions whichcan be obtained by the method of vanishing viscosity is also obtained.展开更多
The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if t...The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.展开更多
The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-de...The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.展开更多
The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and a...The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial initial-boundary value problem for Riemann type of initial-boundary data. Moreover, as examples, we apply the obtained results to the cases of head-on and wide pulse injections and give the expression of the global weak entropy solution.展开更多
Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gra...Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gravitational force and fixed boundary condition when the density connects with vacuum discontinuously.We prove the global existence and the uniqueness of weak solution,requiring less regularity of the initial data.展开更多
In this paper, we study the nonlinear Schr¨odinger equations with derivative. By using the Gal¨erkin method and a priori estimates, we obtain the global existence of the weak solution.
基金supported by the National Natural Science Foundation of China(12301251,12271232)the Natural Science Foundation of Shandong Province,China(ZR2021QA038)the Scientific Research Foundation of Linyi University,China(LYDX2020BS014)。
文摘This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.
文摘The Paraconsistent Many-Valued Similarity (PMVS) method for multi-attribute decision making will be incomplete as a decision model if it is not extended to the realm of group decision-making. Therefore, in this article, our primary objective is to show how the paraconsistent many-valued similarity method can be used to solve group decision-making problems involving choice making or ranking of a finite set of decision alternatives. Moreover, since weights are very important parameters in multi-attribute decision-making, we have introduced the Borda rule to calculate the weights of experts and that of every criterion under consideration. To demonstrate how the proposed method works, a numerical example on energy sources of an economy from the points of view of a group of experts is investigated. Further, we compare the results of this new approach with that of fuzzy TOPSIS group decision-making method to illustrate the robustness and effectiveness of the former.
基金Hong Kong RGC Earmarked Research Grants 14305315,CUHK4041/11P and CUHK4048/13PThe Chinese University of Hong Kong,a Croucher Foundation-CAS Joint Grant,and a NSFC/RGC Joint Research Scheme(N-CUHK443/14)
文摘In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many "singular" times, at which the energy concentration occurs and the director field losses its second order derivatives.
文摘In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {(t, x) | t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.
文摘In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ((φ(ρ))xxφ′(ρ))x with φ(ρ) = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] (α=1/2) to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.
基金The research was supported by the National Natural Science Foundation of China(10361008) Natural Science Foundation of Yunnan Province(2003A002M)
文摘A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.
文摘The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C([0, ∞) × R) ∩ L~∞([0, ∞); H1(R)) under the condition that its initial value belongs to the space H1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.
基金supported by the the NSFC(LY20A010023)a professorship called Qianjiang scholar of Zhejiang Province of China.
文摘In this paper, we study the global existence of weak solutions for the Cauchy problem of the nonlinear hyperbolic system of three equations(1.1) with bounded initial data(1.2). When we fix the third variable s, the system about the variables ρ and u is the classical isentropic gas dynamics in Eulerian coordinates with the pressure function P(ρ, s) = ese-1/ρ,which, in general, does not form a bounded invariant region. We introduce a variant of the viscosity argument, and construct the approximate solutions of(1.1) and(1.2) by adding the artificial viscosity to the Riemann invariants system(2.1). When the amplitude of the first two Riemann invariants(w1(x, 0), w2(x, 0)) of system(1.1) is small,(w1(x, 0), w2(x, 0)) are nondecreasing and the third Riemann invariant s(x, 0) is of the bounded total variation, we obtained the necessary estimates and the pointwise convergence of the viscosity solutions by the compensated compactness theory. This is an extension of the results in [1].
基金supported by National Science Foundation of China (11901020)Beijing Natural Science Foundation (1204026)the Science and Technology Project of Beijing Municipal Commission of Education China (KM202010005027)。
文摘Global in time weak solutions to the α-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to α-model regularization for the three dimension compressible EulerPoisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies γ >4/3.
基金1. The NNSF (0111051400) of Henan Province2. The OYF (0016) of Henan Province.
文摘This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.
基金Supported by National Natural Science Foundation of China(Grant Nos.11831003,12171111)Natural Science Foundation of Beijing in China(Grant No.KZ202110005011)。
文摘The global well-posedness of another class of initial-boundary value problem on two/three-dimensional incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD-Boussinesq equation with the given pressure-velocity’s relation boundary condition for the fluid field,one generalized perfectly conducting boundary condition for the magnetic field and one density/temperature-velocity’s relation boundary condition for the density/temapture at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also proven.
文摘In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin approximation and weak compactness theory.
基金supported by the National Natural Science Foundation of China(61202078)
文摘Weak global navigation satellite system(GNSS) signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS signal acquisition method using re-scaling and adaptive stochastic resonance(SR). The adoption of classical SR is limited to low-frequency and periodic signals. Given that GNSS signal frequency is high and that the periodic feature of the GNSS signal is affected by the Doppler frequency shift, classical SR methods cannot be directly used to acquire GNSS signals. Therefore, the re-scaling technique is used in our study to expand its usage to high-frequency signals and adaptive control technique is used to gradually determine the Doppler shift effect in GNSS signal buried in strong noises. The effectiveness of our proposed method was verified by the simulations on GPS L1 signals. The simulation results indicate that the new algorithm based on SR can reach-181 d BW sensitivity with a very short data length of 1 ms.
文摘The existence of global BV solutions for the Aw-Rascle system with linear damping is considered.In order to get approximate solutions we consider the system in Lagrangian coordinates,then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of[1]we get a sequence of approximate solutions.Finally we show the convergence of this approximate sequence to the weak entropic solution.
文摘We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating sequences generatedby the method of vanishing viscosity. The uniqueness of the generalized solutions whichcan be obtained by the method of vanishing viscosity is also obtained.
基金Project supported by the National Natural Science Foundation of China (No.90511009)
文摘The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11931010,11671384 and 11871047)the key research project of Academy for Multidisciplinary Studies,Capital Normal Universitythe Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(Grant No.007/20530290068)。
文摘The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.
基金supported by the State Key Program of National Natural Science Foundation of China(Grants No.11731008)the National Natural Science Foundation of China(Grants No.10771087)。
文摘The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial initial-boundary value problem for Riemann type of initial-boundary data. Moreover, as examples, we apply the obtained results to the cases of head-on and wide pulse injections and give the expression of the global weak entropy solution.
文摘Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gravitational force and fixed boundary condition when the density connects with vacuum discontinuously.We prove the global existence and the uniqueness of weak solution,requiring less regularity of the initial data.
文摘In this paper, we study the nonlinear Schr¨odinger equations with derivative. By using the Gal¨erkin method and a priori estimates, we obtain the global existence of the weak solution.