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

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 512.05, 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

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H~m convergence rates of solutions of GBBM equations in multi-dimensional spaces

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Progress in Natural Science:Materials International 2009年第9期19卷 1053-1057页

作者： shaomei fang a,*, boling guo b a department of mathematics, South china Agricultural university, Guangzhou 510642, china b Institute of Applied Physics and Computational mathematics, Beijing 100088, china department of mathematics South China Agricultural University Guangzhou 510642 China Institute of Applied Physics and Computational mathematics Beijing 100088 China

In this paper, we study the decay rates of the generalized Benjamin-Bona-Mahony equations in n-dimensional space. By using Fourier analysis for long wave and by applying the energy method for short wave, we obtain the Hm convergence rates of the solutions when the initial data are in the bounded subset of the phase space HmeRnTen P 3T. The optimal decay rates are obtained in our results and are found to be the same as the Heat equation.

关键词： Generalized Benjamin–Bona–Mahony equations Fourier analysis Energy method Optimal convergence rates

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Global weak solutions to a phase-field model for motion of grain boundaries

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Applied mathematics and Mechanics(English Edition) 2022年第11期43卷 1777-1792页

作者： Zixian ZHU boling guo shaomei fang department of mathematics Shanghai UniversityShanghai 200444China Institute of Applied Physics and Computational mathematics Beijing 100088China College of mathematics and Information South China Agricultural UniversityGuangzhou 510642China

We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open *** existence proof is valid in the one-dimensional case.

关键词： solid-solid phase transition phase-field model Galerkin method weak solutions

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Existence of global attractor for a dissipative generalized KdV equation

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Progress in Natural Science:Materials International 2002年第3期 17-21页

作者： fang shaomei and guo boling( department of mathematics, shaoguan university, shaoguan 512.05, china Graduate School, Chinese Academy of Engineering Physics, Beijing 100088, china Institute of Applied Physics and Computational mathematics, Beijing 100088, china) department of mathematics，shaoguan university，shaoguan 512.05，china Graduate School，Chinese Academy of Engineering Physics，Beijing 100088，china Institute of Applied Physics and Computational mathematics，Beijing 100088，china

The global attractor problem of a dissipative generalized KdV equation with periodic boundary condition was studied. The existence of global attractors of this problem was proved by means of a uniform a priori estimat... 详细信息

关键词： generalized KdV equation a priori estimate global attractor.

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