Blow-up And Decay For Pseudo-parabolic P-Laplacian Equation With Logarithmic Nonlinearity

In recent years,with the great development of the subjects such as bi?ology,physical and chemistry,a large number of researchers have devoted their energy in nonlinear pseudo-parabolic partial differential equations.Nonlinear pseudo-parabolic partial differential equations are.widely used in the modern life.Some natural physical science,economic engineering areas and many real life models all use nonlinear partial differential equa-tions to solve problems.In this paper,we study two kinds of the existence,decay and blow-up about nonlinear partial differential equations,which come from the physical and other subjects.It will do great significance and study value.The thesis consists of three sections.Chapter 1 is the preface,which mainly introduces the research back-ground and application status of the pseudo-parabolic equations and the main results of this paper.In Chapter 2,we consider the following nonlinear pseudo-parabolic p-Laplacian equations with one parameter:where ?(?)Rn is a bounded domain with smooth boundary,2<p<n,u0 ?W01.p(?)\{0}..For this equation,we will prove the blow-up in the finite time and the asymptotic behaviors using the method of potential well.In Chapter 3,we consider the following nonlinear pseudo-parabolic p-Laplacian equations with two parameters:where ?(?)Rnis a bounded domain with smooth boundary,2<p<n,u0 ?W01.p(?)\{0}.With the different initial values given in the paper,we prove the blow-up in finite time and decay by the defined functionals and important inequality.Two equations above both satisfy the energy inequality:0?t?T.