一类广义耦合的非线性波动方程组时间周期解的存在性

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The Existence of Time Periodic Solutions for a Damped Generalized Coupled Nonlinear Wave Equations

1.
Department of Mathematics, Shaoguan University, Shaoguan, Guangdong 512005, P. R. China;
2.
Graduate School, China Academy of Engineering Physics, P.O.Box 2101, Beijing 100088, P. R. China;
3.
Institute of Applied Physics and Computational Mathematics, P.O.Box 8009-28, Beijing 100088, P. R. China

摘要: 研究了一类广义耦合的非线性波动方程组关于时间周期解的问题.首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Laray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.
- 非线性波动方程组 /
- 先验估计 /
- 时间周期解
Abstract: The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
- nonlinear wave equations /
- priori estimate /
- time periodic solution

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