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H. Kato. Existence of periodic solutions of the Navier-Stokes equations. Journal of Mathematical Analysis and Applications, 1997, 208(1997): 141-157.

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• 标题: 非线性波动方程的时间周期解 The Time-Periodic Solution for Nonlinear Wave Equation

  作者: 赵维毓, 高平

  关键字: Kuramoto-Sivashinsky方程, 伽辽金方法, Leray-Schauder不动点定理 Kuramoto-Sivashinsky Equation; Galerkin Method; Leray-Schauder Fixed Point Theorem

  期刊名称: 《Advances in Applied Mathematics》, Vol.2 No.1, 2013-02-26

  摘要: 本文利用伽辽金方法，Leray-Schauder不动点定理和先验估计，证明了带周期外力和周期边界的非线性Kuramoto-Sivashinsky方程时间周期解的存在性。In this paper, we study Kuramoto-Sivashinsky equation with periodic boundary condition. The existence and uniqueness of a time-periodic solution is proved by the Galerkin methed and Leray-Schauder fixed point theorem.