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LONG-TIME UNIFORM STABILITY OF SOLUTION TO MAGNETOHYDRODYNAMICS EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 1999年第1期14卷 45-50页

作者： guoboling ZhangLinghai HuangHaiyang InstituteotAppliedPhysicsandComputatiormiMathematics P.O.Box8009Beijing100080. Dept.ofMath. OhioStateUniv.ColumbusOH43210. Dept.ofMath. BeijingNormalUniv.Beijing100875.

The long time uniform stability of solutions to the initial value problems for 2 dimen sional Magnetohydrodynamics equations is studied. The decay estimates are given.

关键词： 1991 MR Subject Classification 35B40 35P10

EXPONENTIAL ATTRACTOR FOR COMPLEX GINZBURG—LANDAU EQUATION IN THREE—DIMENSIONS

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Journal of Partial Differential Equations 2003年第2期16卷 97-110页

作者： guoboling LiDonglong InstituteofAppliedPhysicsandComputationalMathematics P.O.Box8009Beijing100088China GuangxiInstituteofTechnology Liuzou545006China InstituteofAppliedPhysicsandComputationalMathematics P.O.Box8009Beijing100088China

In this paper,we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensions ut=ρu+(1+iγ)△u-1+iμ—|u|^2σu,(1) u(0,x)=u0(x),(2) where u is an unknown complex-value function defined in 3+1 dimensional space-time R^3+1,△ is a Laplacian in R^3,ρ>0,γ,μ are real parameters,Ω∈R^3 is a bounded domain,We show that the semigroup S(t) associated with the problem(1),(2) satisfies Lipschitz continuity and the squeezing property for the initial-value problem(1),(2) with the initial-value condition belonging to H^2(Ω）,therefore we obtain the existence of exponential attractor.

关键词：指数吸引子复Ginzburg-Landau方程偏微分方程半群紧不变集 Lipschitz连续性挤压性

PERSISTENT HOMOCLINIC ORBITS FOR A PERTURBED CUBIC－QUINTIC NONLINEAR SCHROEDINGER EQUATION

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Journal of Partial Differential Equations 2002年第2期15卷 6-36页

作者： guoboling ChenHanlin InstituteofAppliedPhysicsandComputationalMathematics Beijing100088China MainyangNormalCollege Mianyang621000China

In this paper ,the existence of homoclinic orbits,for a perturbed cubic-quintic nonlinear Schroedinger equation with even periodic boundary conditions ,under the geralized parameters conditions is *** specifically,we combine geometric singular perturbation theory,with ,Melnikov analysis and integrable theory to prove the persistences of homoclinic orbits.

关键词：同宿轨非线性Schroedinger方程存在性几何奇异扰动理论 Melnikov分析持久性可移理论解正则性稳定流形

LOCAL WELL-POSEDNESS OF INTERACTION EQUATIONS FOR SHORT AND LONG DISPERSIVE WAVES

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Journal of Partial Differential Equations 2004年第2期17卷 137-151页

作者： HuoZhaohui guoboling GraduateSchool ChinaAcademyofEngineeringPhysicsP.O.Box2101Beijing100088China InstituteofAppliedPhysicsandComputationalMathematics P.O.Box8009Beijing100088China

The well-posedness of the Cauchy problem for the system{iδtu+δx^2u=uv+|u|^2u,t,x∈IR，δtv+δxHδxv=δx|u|^2,u(0,x)=u0(x),v(0,x)=v0(x),is considered. It is proved that there exists a unique local solution (u(x,t), v(x,t))∈C（[0,T);H^s)×C([0,T);Hs^-1/2) for any initial data (u0,v0)∈H^s(IR)×H^s-1/2(IR)(s≥1/4) and the solution depends continuously on the initial data.

关键词：非线性偏微分方程分散波傅里叶规范

EXISTENCE OF PERIODIC SOLUTIONS FOR 3-D COMPLEX GINZBERG-LANDAU EQUATION

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Journal of Partial Differential Equations 2004年第1期17卷 12-28页

作者： LiDonglong guoboling GuangxiUniversityofTechnology Liuzou545006China InstituteofAppliedPhysicsandComputationalMathematics P.O.Box8009Beijing100088China

In this paper, the authors consider complex Ginzburg-Landau equation(CGL) in three spatial dimensions ut=ρu+(1+iγ）△u-(1+iμ）|u|^2σu+f,where u is an unknown complex-value function defined in 3+ 1 dimensional space-time R^3+1，△ is a Laplacian in R^3, ρ > 0, γ μ are real parameters, Ω∈R^3 is a bounded domain. By using the method of Galeerkin and Faedo-Schauder fix point theorem we prove the existence of approximate solution uN of the problem. By establishing the uniform boundedness of the norm ||uN|| and the standard compactness arguments, the convergence of the approximate solutions is considered. Moreover, the existence of the periodic solution is obtained.

关键词：存在性周期解 GINZBERG-LANDAU方程近似解有界性紧性收敛性

THE CLASSICAL SOLUTIONS TO A CAUCHY PROBLEM OF PARABOLIC TYPE COUPLED WITH OPERATORS

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Journal of Partial Differential Equations 2004年第4期17卷 303-315页

作者： KongLinghai guoboling GraduateSchool ChinaAcademyofEngineeringPhysicsP.O.Box2101Beijing100088China CenterforNonlinearStudies InstituteofAppliedPhysicsandComputationalMathematicsP.O.Box8009-28Beijing100088China

We consider the equation ut=Tf[B(x,t,Du,Φu)D^2u]+F(x,t,u,Du,Φu,Ψu) where Φand Ψ are vector-valued *** obtain the existence anduniqueness of classical solution to the equation for a ε-periodic initial *** problem... 详细信息

关键词：周期性退化模型正则化图像降噪不连续性偏微分

EXPONENTIAL ATTRACTOR FOR A CLASS OF NONCLASSICAL DIFFUSION EQUATION

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Journal of Partial Differential Equations 2003年第4期16卷 289-298页

作者： ShangYadong guoboling DepartmentofMathematics GuangzhouUniversityGuangzhou510405China InstituteofAppliedPhysicsandComputationalMathematics P.O.Box8009Beijing100088China

In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make... 详细信息

关键词：指数吸引子扩散方程挤压性渐近行为存在性

THE PERIODIC INITIAL VALUE PROBLEM AND INITIAL VALUE PROBLEM FOR THE MODIFIED BOUSSINEDSA APPROXIMATION

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Journal of Partial Differential Equations 2002年第2期15卷 57-71页

作者： guoboling ShangYadong LaboratoryofCOmputationalPhysics InstituteofAppliedPhysicsandComputationalMathematicsP.O.Box8009Beijing100088China LaboratoryofCOmputationalPhysics InstituteofAppliedPhysicsandComputationalMathemat

The Boussinesq approximation ,where the viscosity depends polynomially on the shear rate ,finds more and more frequent use in geological practice,In this paper ,we consider the periodic initial value problem and inital value problem for this modified Boussinesq approximation with the viscous part of the stress tensor T^v=τ(e)-μ1△e,where the nonlinear function τ(e) satisfies τij(e)eij≥C|e|^p or τij(e)eij ≥C(|e|^2+|e|^p).The existence,uniqueness and regulartiy of the weak solution is proved for p> 2n/(n+2).

关键词：周期初值问题 Boussinesg逼近粘性流体非Newton不可压缩流弱解应力张量存在性唯一性正则性初值问题

HOMOCLINIC ORBIT IN A SIX DIMENSIONAL MODEL OF A PERTURBED HIGHER－ORDER NLS EQUATION

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Journal of Partial Differential Equations 2003年第1期16卷 18-28页

作者： guoboling ChenHanlin InstituteofAppliedPhysicsandComputationalMathematics Beijing100088China SouthwestUniversityofScienceandTechnology Mianyang621000China

In this paper,the perturbed higher-order NLS equation with periodic boundary condition is considered. The existence of the homoclinic orbits for the truncation equation is established by Melnikov analysis and geometri... 详细信息

关键词：同宿轨非线性Schroednger方程摄动周期边界条件存在性模型 Melnikov分析 Fourier截断可积结构双曲不变流形