二维Kuramoto-Sivashinsky方程的非平凡分歧解及其稳定性

Bifurcation and Stability of Nontrivial Solutions to Two-dimensional Kuramoto Sivashinsky Equation

这篇文章讨论了二维K-S方程的分歧现象。对于给定的正整数n_0,m_0,a=n_0~2+m_0~2是一个分歧点,在a附近从平凡解分歧出来的非平凡解枝数依赖于不定方程n^2+m^2=a解的个数,本文给出了解的渐近表示,并讨论了它们的稳定性。

This paper deals with the steady state bifurcation of the K S equation in two space dimensions with periodic boundary value condition and of zero mean. For given positive integer number un, mn a= nn2+mn2, is a bifurcation point. We will give the- asyniptotie expressions of the steady state noutrivial solutions and will discuss the stability of them .