This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
1 Introduction and Preliminaries
In this paper, we are interested in one dimensional viscous Camassa-Holm equation ut-uxxt-γ(uxx-uxxxx)+3uux=uuxxx+2uxuxx+f(x,t), x∈Ω,t＞0, (1) where Ω = [0, L], γ＞ 0 is the const...1 Introduction and Preliminaries
In this paper, we are interested in one dimensional viscous Camassa-Holm equation ut-uxxt-γ(uxx-uxxxx)+3uux=uuxxx+2uxuxx+f(x,t), x∈Ω,t＞0, (1) where Ω = [0, L], γ＞ 0 is the constant viscosity and the forcing term f is ω-periodic in time t.We shall prove that under a periodic boundary condition u(x, t) is ω-periodic in the spatial variable x,Eq.(1) has a time periodic solution by using the Galerkin method and Leary-Schauder fixed point theorem (similar to the method of [4]).展开更多
基金Supported by Natural Science Foundation of China (10471047)Natural Science Foundation of Guangdong Province (05300162)
文摘This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
基金The projected by the Nation Natural Science Foundation of China(No.10171032)
文摘1 Introduction and Preliminaries
In this paper, we are interested in one dimensional viscous Camassa-Holm equation ut-uxxt-γ(uxx-uxxxx)+3uux=uuxxx+2uxuxx+f(x,t), x∈Ω,t＞0, (1) where Ω = [0, L], γ＞ 0 is the constant viscosity and the forcing term f is ω-periodic in time t.We shall prove that under a periodic boundary condition u(x, t) is ω-periodic in the spatial variable x,Eq.(1) has a time periodic solution by using the Galerkin method and Leary-Schauder fixed point theorem (similar to the method of [4]).
