The Global Attractor For A Class Coupled Of Nonlinear Abstract Differential Equations With Memory Term

Nonlinear evolution equations are the performance of many nonlinear problems in mathematics. At present, the wave equation is a very active topic,especially, the wave equation with memory term has been increasingly attention. As time goes on, the increasing evolution equation. The study of these problems and solve eventually boil down to the existence of the overall solution of the nonlinear differential equation and the attractor. These are the precondition of the investigation of infinite dimensional dynamical systems. Power system research purpose is to understand all sorts of change with time in the nature of the law of development. In application,infinite dimensional dynamical system is more general than finite dimensional dynamical system. Infinite dimensional power system research is spatial chaos phenomenon, chaos is a complicated and difficult to understand the concept. Because of the absorbency and invariance, whole attractor is describing one of the best tools in the chaos and can commendably describe the long time behavior of the systems.In this paper, we studied the existence of the global attractor for a class coupled of nonlinear abstract differential equations with memory term, that is, the following coupled equations under the initial conditionsWe show the proof the existence of the global attractor, where Ω is Rn with smooth boundary of a bounded area, A is a positive self-adjoint operator defined in Hilbert space L2(Ω), function M satisfy certain conditions.The paper is arranged as followsIn Chapterl, the item associated with this article has the memory of nonlinear partial differential equation (group) the development and research of present situation has carried on the brief summary and review;In Chapter2, we gave some important concepts, lemmas and assumptions relate to the paper, and explained part of the symbol for this article;In Chapter3, we used Faedo-Galerkin method to show the existence of the global attractor for the problems(l)-(2) in a Hilbert space framework;In Chapter4, based on semigroup theory, we proved the existence of the whole attractor the system;In Chapter5, for this article, we did some summaries and made some prospects for the future of nonlinear partial differential equation (group) with memory.