非线性Sobolev-Galpern方程的有限维整体吸引子(英文)  

Finite Dimensional Global Attractors for Nonlinear SobolevGalpern Equations

作　　者：尚亚东[1] 房少梅[2] 

机构地区：[1]广州大学数学系,广东广州510405 [2]韶关大学数学系,广东韶关512005

出　　处：《应用数学》2003年第4期122-129,共8页Mathematica Applicata

基　　金：SupportedbyNNSFofChina(10 2 710 34 )

摘　　要：本文研究非线性Sobolev Galpern方程解的渐近性态 .首先证明了该方程在H2 (Ω)∩H1 0 (Ω)中整体弱吸引子的存在性 ,然后利用一个能量方程证明了整体弱吸引子实际上是整体强吸引子 .In this paper,we study the asymptotic beha vio r of solutions for the nonlinear SobolevGalpern equations.We first show the ex istence of the global weak attractor in H 2(Ω)∩H 1 0(Ω) for the equati ons.And then by an energy equation we prove that the global weak attractor is ac tually the global strong attractor.The finite dimensionality of the global attra ctor is also established.

关 键 词：非线性SOBOLEV-GALPERN方程 整体吸引子 解 渐近性 能量方程 弱收敛性 有限维性 初边值问题 

分 类 号：O175.29[理学—数学]