Research On The Global Existence And Blow-up Properties Of The Solutions Of Two Types Of Quasi-linear Parabolic Equations With Memory Term

In this work,we consider the global existence and bounds for blow-up time of solutions of two kinds of quasilinear parabolic equations with a memory term.In chapter 1,we consider the global existence and bounds for blow-up time of solutions to a class of quasilinear parabolic equations with a memory where ? is a bounded domain of Rn(n>2)with smooth boundary(?)?,q>2,the initial value u0 E H01(?)and the parameters a,b and the functions g,k satisfy certain conditions.We obtain the local and global existence of the solution by Galerkin's method.We prove finite-time blow-up of the solution for initial data at arbitrary ener-gy level and obtain upper bounds for blow-up time by using the concavity method.In addition,by means of differential inequality technique,we obtain a lower bound for blow-up time of the solution if blow-up occurs.In chapter 2,we consider the global existence,a general decay of the energy func-tion and bounds for blow-up time of solutions to a fourth order quasilinear parabolic equations with a memory term where p?2,q>1,?is a bounded domain of Rn(n? 1)with smooth boundary(?)?,v is the outward normal on(?)?,g is a C1-function and the initial value u0?H02(?).