Asymptotic Behavior Of Solutions To Two Kinds Of Nonlinear Parabolic Equations

Infinite dimensional dynamical system has wide applications in Physical,Chemistry,fluid dynamics,atmospheric science and other fields,of which the main concern is to study long time behavior of global solutions to various non-linear dissipative evolutionary equations.Dissipative systems arise extensively in physics,Chemistry,biology and the other various areas in science and tech-nology.Thus,the study on large time behaviors of solutions to dissipative systems is of great theoretical and practical importance.In this thesis,we will take reaction diffusion equations with dynamical boundary conditions and ir-regular data,as well as a class of nonuniform nonlinear parabolic equations as the prototype of models to study the asymptotic behavior of solutions of the global solutions,special attentions will be paid on the studying the existence of global attractors.This paper is divided into five chapters.In Chapter one,we provide the outline on background and advances in the following four aspects:autonomous dynamical systems;reaction diffusion equations with dynamical boundary con-ditions;elliptic and parabolic equa,tion with irregular data;and finally the non-uniformly parabolic equations.In Chapter two,we provide some func-tion spaces,marks and some important inequalities,which are involved in this paper.The third and the forth chapters are the main parts of the thesis.In Chap-ter three,we investigate the existence of global solutions and their large time behavior for reaction-diffusion equations with dynamical boundary conditions and irregular data We first establish the existence and uniqueness result to the problem with regular data.Then using smooth approximations,we prove the existence and uniqueness of the entropy solutions to the problem.Finally,we prove the existence of global attractor in L1(?,dv)for the semigroup generated by the entropy solution.In Chapter four,we consider the asymptotic behavior of solutions to the following non-uniformly parabolic equations.where ? is a bounded domain of RN(N ? 2)with Lipschitz boundary ?.Under suitable assumption on the initial data and forcing terms,we prove the existence and uniqueness of weak solution by using the Rothe method.Then we prove the solution semigroup admits a global attractor in proper space.In Chapter five,we summarize the work of this paper and provide the future research plan.