Kuramoto-Sivashinsky方程解的定性分析

基金项目: 国家自然科学基金(19871051); 中国博士后科学基金资助项目(499772161)

Qualitative Analysis for the Solution of Kuramoto-Sivashinsky Equation

1.
Department of Applied Mathematics, University of Information Engineering, Zhengzhou 450002, P R China;
2.
Department of Mathematics, Shandong University, Jinan 250100, P R China

摘要: 研究Kuramoto-Sivashinsky方程的两种初边值问题,运用Galerkin方法给出一系列先验估计结果,得到广义解和古典解的存在唯一性、正则性及某些条件下的渐近性质。
- Kuramoto-Sivashinsky方程 /
- 初边值间题 /
- 广义解 /
- 古典解 /
- 渐近性质
Abstract: In this paper, two kinds of initial boundary value problems for Kuramoto-Sivashinsky equation are considered. Some prior estimates are derived by Galerkin methods. The existence, uniqueness and regularities of the generalized global solutions and the classical global solutions for the equation are proved. Morever, the asymptotic behavior of these solutions are considered under some conditions.
- Kuramoto-Sivashinsky equation /
- initial boundary value problems /
- generalized global solution /
- classical global solution /
- asymptotic behavior

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