一类非线性发展方程的整体吸引子  

Existence of Global Attractors for a Class of Nonlinear Evolution Equations

作　　者：孙晶晶 张建文 SUN Jingjing;ZHANG Jianwen(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,太原030024

出　　处：《太原理工大学学报》2018年第2期300-307,共8页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目(11172194);山西省自然科学基金资助项目(2014011005-4;2015011006)

摘　　要：由Sobolev嵌入定理及一些先验估计,应用Galerkin方法研究了一类非线性发展方程的解的存在性和唯一性,并通过Gronwall引理和验证条件(C)证明了该方程在空间H_0~1(Ω)×H_0~1(Ω)中整体吸引子的存在性,其中非线性项f(u)满足临界指数增长条件。In this paper,some priori estimates are obtained by the Sobolev embedding theorem for studying the existence and uniqueness of solutions of a generalized nonlinear equation via Galerkin method.It is proved that under the natural assumptions,these equations possess the global attractors in H 1 0(Ω)×H 1 0(Ω)by using Gronwall lemma and verifying conditions(C),where the nonlinear term f(u)satisfies a critical exponential growth condition.

关 键 词：GALERKIN方法 先验估计 非线性发展方程 整体吸引子 

分 类 号：O175.29[理学—数学]