二维空间中半线性摄动波动方程初值问题解的渐近理论

基金项目: 四川省青年基金资助课题(1999-09)

The Asymptotic Theory of Initial Value Problems for Semilinear Perturbed Wave Equations in Two Space Dimensions

1.
Department of Mathematics, Sichuan Normal University, Chengdu 610066, China;
2.
Department of Technology, Xichang Teacher's College, Xichang, Sichuan 630025, China

摘要: 研究二维空间中具初值问题的半线性波动方程解的渐近理论,在二次连续的古典空间中得到了形式近似解的渐近合理性在长时间范围内成立,这一结果描述了渐近解的长时间存在性.作为所得到的渐近理论的应用,对二维空间中的一个特殊波动方程作出了分析.
- 半线性波方程 /
- 渐近性 /
- 长时间 /
- 应用
Abstract: The asymptotic theory of initial value problems for semilinear wave equations in two space dimensions was dealt with. The well-posedness and vaildity of formal approximations on a long time scale were discussed in the twice continuous classical space. These results describe the behavior of long time existence for the validity of formal approximations. And an application of the asymptotic theory is given to analyze a spacial wave equation in two space dimensions.
- semilinear wave equation /
- asymptotics /
- long time scale /
- application

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