The Initial-boundary Value Problem For A Class Of Semilinear Pseudo-parabolic Equations

Consider the initial boundary value problem for the semilinear pseudo-parabolic equationWhere ?(?)Rn is a bounded domain with enough smooth boundary,p?2 andThe above equations can be used to describe nonlinear,dispersion,one-way propagation of long wave and population aggregation,and also to analyze the non-stationary process in the edge semiconductor.The current research on this equation group mainly considers the field of physics,and the research on weak solutions is relatively inadequate,and these research results cannot fully reveal many important properties of the pseudo-parabolic equation.Therefore,this article is devoted to considering the overall existence of the weak solution under which initial value and under which conditions the solution is blowing up,and to study the vacuum isolation phenomenon of the solution.The content of this paper is arranged as followsIn Chapter one,the physical background of parabolic equation is briefly reviewed,and the previous research results,research methods and main conclusions are used in this paper are introducedIn Chapter two,the preliminary knowledge of potential well theory is given,and the related properties of potential well family are obtainedIn Chapter three,the priori estimate of weak solution is established by using invariant set W,and the existence and uniqueness of weak solutions of the problem are proved by the Galerkin embedding theorem,Growall inequality and Aubin compactness lemmaIn Chapter four,by means of the invariant set of solutions,the vacuum isolation of solutions to the problem is studiedIn Chapter five,by using convex operator method,the blow-up of weak solution is obtained.