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The unconditional stable and convergent difference methods with intrinsic parallelism for quasilinear parabolic systems

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Science China Mathematics 2004年第3期47卷 453-472页

作者： ZHOU Yulin YUAN Guangwei SHEN Longjun Laboratory of computational physics, center of nonlinear studies, institute of applied physics and computational Mathematics, Beijing 100088, China 1. Laboratory of computational physics Center of Nonlinear Studies Institute of Applied Physics and Computational Mathematics 100088 Beijing China

A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2 (2,1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.

关键词： difference scheme, intrinsic parallelism,quasilinear parabolic system, convergence, stability.

GENERAL DIFFERENCE SCHEMES WITH INTRINSICPARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OFDIVERGENCE TYPE

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Journal of computational Mathematics 1999年第4期17卷 337-352页

作者： Yu-lin Zhou Guang-wei Yuan(Laboratory of computational physics, center of nonlinear studies, institute of applied physics and computational Mathematics, P.O. Box 8009, Beijing 100088, China) Laboratory of computational physics Center of Nonlinear Studies Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.

关键词： difference scheme intrinsic parallelism semilinear parabolic system convergence

Long time behavior for damped generalized coupled nonlinear wave equations. Ⅱ.Unbounded domain

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Communications in nonlinear Science and Numerical Simulation 2001年第2期6卷 107-110页

作者： Shaomei FANG and Boling GUO Department of Mathematics, Shaoguan University, Shaoguan 512005, China Graduate School, China Academy of Engineering physics, Beijing 100088, China center for nonlinear studies, institute of applied physics and computational Department of Mathematics Shaoguan University Shaoguan 512005 China Graduate School China Academy of Engineering Physics Beijing 100088 China center for nonlinear studies Institute of Applied Physics and Computational mathematics Beijing 100088 China

In this paper, by using a priori estimates in the weighted space, the existence of the global attractor for the damped generalized coupled nonlinear wave equations in an unbounded domain is obtained.

关键词： unbounded domain weighted space attractor

NEUMANN PROBLEM FOR THE LANDAU-LIFSHITZ-MAXWELL SYSTEM IN TWO DIMENSIONS

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Chinese Annals of Mathematics,Series B 2001年第4期22卷 529-540页

作者： GUO BOLING, DING SHIJIN center of nonlinear studies, institute of applied physics and computational Mathematics, P. O. Box 8009, Beijing 100088, China. E-mail: gbl@ *** center of nonlinear studies Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China

This paper is concerned with the global existence and the partial regularity for the weak solution of the Landau-Lifshitz-Maxell system in two dimensions with Neumann boundary conditions.

关键词： Landau-Lifshitz-Maxwell system Neumann problem Global existence

Stability of Travelling Wave Solutions of the Derivative Ginzburg-Landau Equations1,2

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Communications in nonlinear Science and Numerical Simulation 1997年第3期 20-26页

作者： Boling Guo, Bainian Lu , Guihua Wan (Laboratory of computational physics, center for nonlinear studies, institute of applied physics and computational Mathematics, Beijing, 100088, P.R. China) (institute of computational and App

ＳｔａｂｉｌｉｔｙｏｆＴｒａｖｅｌｉｎｇＷａｖｅＳｏｌｕｔｉｏｎｓｏｆｔｈｅＤｅｒｉｖａｔｉｖｅＧｉｎｚｂｕｒｇＬａｎｄａｕＥｑｕａｔｉｏｎｓ１，２１ＴｈｅｐａｐｅｒｗａｓｒｅｃｅｉｖｅｄｏｎＳｅｐｔ．８，１９９７... 详细信息

ＳｔａｂｉｌｉｔｙｏｆＴｒａｖｅｌｉｎｇＷａｖｅＳｏｌｕｔｉｏｎｓｏｆｔｈｅＤｅｒｉｖａｔｉｖｅＧｉｎｚｂｕｒｇＬａｎｄａｕＥｑｕａｔｉｏｎｓ１，２１ＴｈｅｐａｐｅｒｗａｓｒｅｃｅｉｖｅｄｏｎＳｅｐｔ．８，１９９７２ＴｈｅＰｒｏｊｅｃｔＳｕｐｐｏｒ...

关键词： Ginzburg Landau equation travelling wave solution stability Chern’s number unstable augmented bundle.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2 and Cheng Caozong1(1. College of applied Sciences, Beijing University of Technology, Beijing 100022, China 2. center for nonlinear studies, institute of applied physics and computational Mathematics, Beijing 100088, China) College of applied Sciences Beijing University of Technology Beijing 100022 China center for nonlinear studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

Steady State Solution for the Weakly Damped Forced Korteweg-de Vries Equation

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Communications in nonlinear Science and Numerical Simulation 1998年第2期 71-76页

作者： Boling GUO * and Guoguang LIN **, * (center for nonlinear studies,institute of applied physics and computational Mathematics, Beijing 100088, China) ** (Graduate School of China Academy of Engineering physics, Beijing 100

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｗｅａｋｌｙｄａｍｐｅｄｆｏｒｃｅｄＫｏｒｔｅｗｅｇｄｅＶｒｉｅｓｅｑｕａｔｉｏｎｓｗａｓｓｔｕｄｉｅｄ［１］ｕｔ＋ｕｘｘｘ＋γｕ＋βｕｕｘ＝ｆ（ｘ）（１ｗｈｅｒｅγ＞０ａｎｄβａｒｅ... 详细信息

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｗｅａｋｌｙｄａｍｐｅｄｆｏｒｃｅｄＫｏｒｔｅｗｅｇｄｅＶｒｉｅｓｅｑｕａｔｉｏｎｓｗａｓｓｔｕｄｉｅｄ［１］ｕｔ＋ｕｘｘｘ＋γｕ＋βｕｕｘ＝ｆ（ｘ）（１ｗｈｅｒｅγ＞０ａｎｄβａｒｅｒｅａｌｃｏｎｓｔａｎｔｓ．Ｗｅｃ...

关键词： KdV equation steady state solution third order boundary value problem asymptotic behavior

非牛顿粘性不可压流方程的近似惯性流形(英文)

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数学研究 1999年第4期 327-340页

作者：郭柏灵林国广北京应用物理与计算数学研究所!北京100088 云南大学数学系!昆明650091

本文利用对非牛顿粘性不可压缩流方程对时间 t的解析性和长时间渐近性估计 ,具体构造了它的近似惯性流形 ,并得出收敛阶估计 .

关键词：近似惯性流形非牛顿粘性不可压缩流

nonlinear　GALERKIN　METHODS　FOR　SOLVING　TWO　DIMENSIONAL　NEWTON－BOUSSINESQ　EQUATIONS

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Chinese Annals of Mathematics,Series B 1995年第3期16卷 379-390页

作者： GUO BOLING(center for Nonlineajr studies,institute of applied physics and computational Mathematics, Beijing100088, China.) 北京应用物理和计算数学所北京

The nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations are *** existence and uniqueness of global generalized solution of these equations, and the convergence of approximate solutions a... 详细信息

关键词： nonlinear Galerkin method Newton-Boussnesq equations A uniformly prior estimate.