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BLOW-UP SOLUTIONS OF TWO-COUPLED NONLINEAR SCHR?DINGER EQUATIONS IN THE RADIAL CASE
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作者 白欠欠 李晓光 张莉 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1852-1864,共13页
We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R ... We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R N,t0.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu[10]by dropping the hypothesis of finite variance((|x|u_(0),|x|v_(0))∈ L^(2)(R^(N))×L^(2)(R^(N))). 展开更多
关键词 SchrOdinger equations radial symmetry blow-up virial identity
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SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS
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作者 张学梅 阚士坤 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1175-1194,共20页
Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro... Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered. 展开更多
关键词 singular p-Laplacian equation boundary blow-up sub-supersolution method EXISTENCE nonexistence and estimates sufficient and necessary conditions
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BLOW-UP SOLUTIONS FOR A CASE OF b-FAMILY EQUATIONS 被引量:3
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作者 Zongguang LI Rui LIU 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期910-920,共11页
In this article, we study the blow-up solutions for a case of b-family equations.Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up ... In this article, we study the blow-up solutions for a case of b-family equations.Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up solutions: the hyperbolic blow-up solution, the fractional blow-up solution, the trigonometric blow-up solution, the first elliptic blow-up solution, and the second elliptic blow-up solution. Not only are the expressions of these blow-up solutions given, but also their relationships are discovered. In particular, it is found that two bounded solitary solutions are bifurcated from an elliptic blow-up solution. 展开更多
关键词 b-family equation blow-up solutions qualitative theory bifurcation method
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Global solution and blow-up solution for a nonlinear damped beam with source term 被引量:2
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作者 WU Jie-qiong LI Sheng-jia School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第4期447-453,共7页
A nonlinear damped system with boundary input and output, which also has source term, is studied in this paper. It is proved that under some conditions the system has global solution and blow-up solution.
关键词 Nonlinear hyperbolic system boundary input and output global solution blow-up solution.
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LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL 被引量:1
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作者 朱世辉 张健 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期1181-1192,共12页
This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the li... This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN |x|^2|u|^2dx 〈 +∞)}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that |u(t, x)|^2→ ||Q||L^2 2 δx=x1 as t → T. 展开更多
关键词 Nonlinear Schroedinger equation Stark potential blow-up solution limiting behavior mass concentration
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Exact Blow-up Solutions forMultidimensional Landau--Lifshitz Equations 被引量:7
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作者 郭柏灵 韩永前 杨干山 《数学进展》 CSCD 北大核心 2001年第1期91-93,共3页
关键词 多维LANDAU-LIFSHITZ方程 精确blow-up 边值问
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Global and Blow-up Solutions to a p-Laplace Equation with Nonlocal Source and Nonlocal Boundary Condition 被引量:1
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作者 GUO BIN WEI YING-JIE GAO WEN-JIE 《Communications in Mathematical Research》 CSCD 2010年第3期280-288,共9页
This paper deals with an evolution p-Laplace equation with nonlocal source subject to weighted nonlocal Dirichlet boundary conditions. We give sufficient conditions for the existence of global and non-global solutions.
关键词 nonlocal boundary condition evolution p-Laplace nonlocal source blow-up
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A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations
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作者 Chien-Hong Cho 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第4期475-498,共24页
We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we pro... We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we propose a rule for a time-stepping,which is a variant of what was successfully used in the case of nonlinear parabolic equations. A numerical blow-up time is defined and is proved to converge, under a certain hypothesis, to the real blow-up time as the grid size tends to zero. 展开更多
关键词 Finite difference method nonlinear wave equation blow-up
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Blow-up Solutions to a Viscoelastic Fluid System and a Coupled Navier–Stokes/Phase-Field System in R^(2)
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作者 ZHAO Li-Yun GUO Bo-Ling HUANG Hai-Yang 《Chinese Physics Letters》 SCIE CAS CSCD 2011年第6期21-23,共3页
The explicit solutions to both the Oldroyd-B model with an infinite Weissenberg number and the coupled Navier–Stokes/phase-field system are constructed by the method of separation of variables.It is found that the so... The explicit solutions to both the Oldroyd-B model with an infinite Weissenberg number and the coupled Navier–Stokes/phase-field system are constructed by the method of separation of variables.It is found that the solutions blow up in finite time. 展开更多
关键词 INFINITE SEPARATION solutions
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GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY 被引量:1
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作者 丁时进 李颖花 王喻 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期195-214,共20页
This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depen... This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth. 展开更多
关键词 Navier-Stokes/Allen-Cahn system density-dependent viscosity free boundary global solutions
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Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation
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作者 巩乾坤 王惠 王云虎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期409-416,共8页
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ... This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs. 展开更多
关键词 lump solution rogue wave solution breather wave solution (2+1)-dimensional Hirota-Satsuma-Ito equation
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PDE Standardization Analysis and Solution of TypicalMechanics Problems
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作者 Ningjie Wang Yihao Wang +1 位作者 Yongle Pei Luxian Li 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期171-186,共16页
A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach throu... A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed. 展开更多
关键词 Three standard forms expression input PDE module deflection solution stress solution
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THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE
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作者 金可 石影 谢华飞 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期583-608,共26页
In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are... In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems. 展开更多
关键词 Schrödinger system ground states solutions bound state solutions
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Solution approximations for a mathematical model of relativistic electrons with beta derivative
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作者 Ibrahim Yalcinkaya Orkun Tasbozan +1 位作者 Ali Kurt Hijaz Ahmad 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期469-485,共17页
The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with... The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling. 展开更多
关键词 Klein-Fock-Gordon(KFG)equation beta derivative semi-analytical solution exact solution
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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation BIFURCATIONS Phase Portrait Analytical Periodic Wave solution Periodic Cusp Wave solution
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Analytic Solutions for Hindered Rotation Quantum Problem
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作者 Mirco Ragni 《Applied Mathematics》 2024年第10期709-718,共10页
Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematic... Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematical advance in the description of physical phenomena described by the second derivative operator associated with a divergent interaction potential and, being analytical, guarantee the optimal interpretation of such phenomena. 展开更多
关键词 Analytics solutions Schrodinger Equation Interaction Potential
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Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition
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作者 Mohamed Karimou Gazibo Duni Yegbonoma Frédéric Zongo 《Applied Mathematics》 2024年第7期455-463,共9页
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
关键词 Lebesgue and Sobolev Spaces with Variable Exponent Weak solution Entropy solution Degenerate Parabolic-Hyperbolic Equation Conservation Law Leray Lions Type Operator Neumann Boundary Condition Existence Result
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Malargüe Site Remediation:A Successful Solution for Uranium Mill Tailings
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作者 BARARI E DíAZ J G +1 位作者 GIOMIA KEMPF R A 《原子能科学技术》 EI CAS CSCD 北大核心 2024年第10期2088-2094,共7页
Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with ... Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with its legal responsibilities,decides to implement a restoration project for all sites related to the mining and processing of uranium ores.The Malargüe Site is located within the Province of Mendoza in the city of Malargüe.It is the first site to successfully complete its remediation.The activities consist of relocation of tailings to an engineering repository.The tailings management(encapsulation) and rehabilitation of the area was finished in June 2017.The remediation alternative for the ore tailings was selected after conducting comparative studies and submitted the project to the society for consideration.The objective of the encapsulation of the mineral tails is to isolate them from the environment,also proceeding with the decontamination and rehabilitation of the area (landscaping,post-closure monitoring and 20 years monitoring period).Encapsulation consisted of the construction of a containment cell for the mine tailings,to isolate them and prevent pollutants from entering the environment through the transfer routes.To clean the impacted areas,the soil was removed,it was incorporated into the encapsulation,and the filling was carried out with natural soils from the area.Remediation prevents radon transfer to the environment,as ^(222)Ra is an alpha emitter with a half-life of four days,which produces its own radioactive progeny.Radon progeny are solids,and when a ^(222)Ra nucleus emits an alpha particle into the air,the resulting ^(218)Po nucleus,momentarily electrically charged,adheres to any dust particle.Remediation prevents the discharge into the air containing radon and also containing dust particles charged with intensely radioactive radon progeny.The tasks mentioned make it possible to decrease radon emanation,reduce radiological risks to the public and prevent the entry of rainwater into the system.In addition,the containment system prevents the discharge of contaminated liquids into the environment,avoiding contamination of the groundwater.All these activities are according to the concepts of sustainability. 展开更多
关键词 REMEDIATION radionuclide transfer TAILINGS ENCAPSULATION solution sustainable
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GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE
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作者 王晓闪 王忠谦 贾哲 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期909-924,共16页
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
关键词 global weak solutions attraction-repulsion P-LAPLACIAN logistic source
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Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions
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作者 孙志强 侯国林 +1 位作者 乔艳芬 刘金存 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第1期581-590,共10页
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o... A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method. 展开更多
关键词 Hamiltonian system symplectic elasticity QUASICRYSTALS analytic solution state function
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