Pullback And Uniform Exponential Attractors For The Non-autonomous Reversible Gray-Scott System

This thesis investigates the existence of pullback and uniform exponential attractors for the non-autonomous three-component reversible Gray-Scott system. Following is the structure of this thesis.In the first chapter, initially we introduce the research status of infinite-dimensional dynamical systems (mainly non-autonomous), then we discuss the necessity and im-portant meaning of considering pullback and uniform exponential attractor for non-autonomous infinite-dimensional dynamical systems. Moreover, we introduce the research status of Reversible Gray-Scott System. Eventually we introduce main content of this paper.In the second chapter, it mainly introduces some preliminary knowledge, including some related definitions and theorems, and some inequalities of this paper.In the third chapter, it mainly study the existence of a pullback exponential attractor for the nonautonomous three-components reversible Gray-Scott system which was used to simulate two reversible chemical reactions. When the time-depending external forces are translation bounded in the space of locally integrable functions, we first present the existence and uniqueness of solutions for the system; then we prove the ultimately uniform boundedness of solutions in the state space and a more regular space; next we prove the Lipschitz continuity of solutions in a family of positive invariant closed subsets and we make an "tail estimate" on the difference between two solutions; finally we obtain the existence of a pullback exponential attractor for the system by using a criterion concerning the existence of a pullback exponential attractor, moreover, we get an upper bound of the fractal dimension of this attractor and an estimation of exponentially attracting any bounded set.In the fourth chapter, it mainly study the existence of a uniform exponential attrac-tor for the nonautonomous three-components reversible Gray-Scott system with quasi-periodic external forces on bounded domain which was used to simulate two reversible chemical reactions. We first present the existence and uniqueness of solutions for the system; then we prove the existence of uniform attractor for this system; then we prove the existence of a uniform exponential attractor for this system basing on a carefully "end estimate" of solutions. moreover, we get an upper bound of the fractal dimension of this attractor and an estimation of exponentially attracting any bounded set.In the fifth chapter, we give a summary and prospect for this thesis.