Study On The Properties Of Solutions For Two Classes Nonlinear Partial Differential Equations

Partial differential equation is a very important branch of mathematics in the field of Mathematics.With the development of science,we find nonlinear partial differential equations are becoming more and more closely related to other disciplines,especially in physics,biology,economics and other disciplines.However,for many nonlinear partial differential equations,exact solutions can not be obtained.Therefore,qualitative study of some properties of solutions has also become an effective way to solve nonlinear partial differential equations.In this thesis,we mainly study the properties of solutions of two kinds of nonlinear partial differential equations.In chapter 1,we provide some research status about wave equation and heat equation with strong damping,nonlinear source term and delay.In chapter 2,we discuss the property of solution for the quasilinear viscoelastic wave equation with strong damping and source term.Under suitable assumptions on the initial data and the relaxation function,we establish a blow-up result of a solution for negative initial energy and some positive initial energy if the influence of the source term is greater than the dissipation.We show that the solution exists globally for any initial data if the influence of dissipation is greater than the source term.In chapter 3,we study the asymptotic behavior of solution for thermoelastic system with distributed delay and source term.Firstly,we prove the existence of solution of thermoelastic system by Faedo-Galerkin method.Next,we define the energy functional.Then,we deal with the various kinds of energy functional by the multiplier method.Finally,we prove the asymptotic behavior of the solution.