Backward Compact Pullback Attractors For Non-autonomous Kuramoto-Sivashinsky Equation

In this paper,we use an existence theorem of the pullback attractor for the tight term,which proves that there is a unique tight pullback attraction for the nonautonomous Kuramoto-Sivashinsky equation under the assumption that the ex-ternal force term slowly increases about ?.The Gronwa lemma of the latter term is the key to prove the progressive compactness of the non-autonomous system.This paper we mainly study the following forms of Kuramoto-Sivashinsky equations with non-autonomous terms in interval I=?-l/2,l/2?.u_t + vD⁴u + D²u + uDu = g?t,x??x,t?? I× R Diu?t,l/2?=Diu?t,-l/2?i=0,1,2,3 ?_-l/2^l/2u?t,x?= 0 u?x,0?= u₀?x?The paper contains three chapters:· In the first chapter:This chapter mainly introduces the development status of the stochastic dynamic system,pulls back the attractor,the research status of the Kuramoto-Sivashinsky equation at home and abroad,summarizes the references briefly,and points out the main contents of the research done in this paper.Meaning,at the same time,sort out the basic knowledge and some basic inequalities related to this paper.· In the second Chapter:This chapter mainly uses Galerkin approximation method to obtain the unique solution of K-S equation with u = u?,s,u0?,and this solution can generate a continuous stochastic dynamic system.· In the third Chapter:This chapter mainly introduces that under the giv-en assumptions,the non-autonomous power system generated by the solu-tion of non-autonomous K-S equations has an increasing bounded absorption set.Then using the consistent Gronwa lemma of the post-item,we prove a post-item estimation of the K-S equation in H space and prove that the non-autonomous process produced by the equation is asymptotically tight in the given space.