Existence Of Attractors In Non-Classical Reaction Diffusion Equations With Distributed Derivatives

In this paper,we mainly study the exponential attractors and global attractors of nonclassical reaction diffusion equations with derivative terms.first,the term ?ut in the system makes the solution semigroups no longer possess the higher regularity in the classical reaction diffusion equation,therefore,the compactness of the system can not be directly obtained by using the Sobolev compact embedding theorem;Secondly,we can not obtain its dissipative results by the standard attractor theory because the system contains a positive decreasing function;Finally,the nonlinear term of the system satisfies the critical exponential growth condition,these all make it difficult to study in this paper.Specific arrangements are as follows:The first chapter introduces the background and research status of the reaction diffusion equation at home and abroad are briefly expounded.The second chapter,the basic definitions,theorems,lemmas,space and common inequalities used in this paper are given.In the third chapter,we study the existence of exponential attractors for a class of nonclassical reaction-diffusion equations with distributed derivatives when the nonlinear term satisfies the critical exponential growth condition by using the extruding property method.In the fourth chapter,the existence of global attractors for a class of nonclassical reactiondiffusion equations with distributed derivatives on unbounded domains is studied.Firstly,it is proved that the system has bounded absorption sets in L2(Rn);Secondly,by using the decomposition technique of the solution,the uniform decay estimates of inner region and outer region are discussed,the ?-limit compactness of the solution semigroup is obtained,thus the global attractor of reaction-diffusion equation in the unbounded domain is obtained.The fifth chapter,that make a briefly summarizes the contents of this research,and puts forward some corresponding problems for further exploration.