﻿ 强阻尼波动方程的近似惯性流形 Approximate Inertial Manifold of Strongly Damped Wave Equation

Pure Mathematics
Vol.05 No.06(2015), Article ID:16436,6 pages
10.12677/PM.2015.56040

Approximate Inertial Manifold of Strongly Damped Wave Equation

Sufang Zhang, Jianwen Zhang

College of Mathematics, Taiyuan University of Technology, Taiyuan Shanxi

Received: Nov. 4th, 2015; accepted: Nov. 21st, 2015; published: Nov. 27th, 2015

ABSTRACT

In this paper, the global attractor approximation by smooth manifold is considered in strongly damped equation. A nonlinear approximate inertial manifold of strongly damped wave equation is constructed. The order of approximation of the inertial manifold to the global attractor is obtained．

Keywords:Strongly Damped, Approximate Inertial Manifold, Wave Equation

1. 引言

(1)

2. 预备知识

，则为无界正自共轭算子，原方程(1)可化为如下的微分系统：

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

3. 主要结果及其证明

(10)

(11)

(12)

(13)

(14)

(15)

(16)

，此时(14)式可以重写为

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

Approximate Inertial Manifold of Strongly Damped Wave Equation[J]. 理论数学, 2015, 05(06): 278-283. http://dx.doi.org/10.12677/PM.2015.56040

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