Asymptotic Behavior Of Solutions For Quasilinear Random Viscoelastic Wave Equations

In this paper,we study the properties of stochastic quasilinear viscoelastic wave equations,including existence,uniqueness,blow-up and asymptotic stability.The main contents of this paper are divided into the following four chapters:In the first chapter,we introduce the research background,research significance and status of partial differential equations.In the second chapter,the initial boundary value problem of stochastic quasilinear viscoelastic wave equation with nonlinear damping |ut|q-2ut and source terms |u|p-2 u driven by multiplicative noise is discussed.First,the existence and uniqueness of the local solution are obtained by the iterative method and the truncation function method;further,when q?p,the global solution is obtained;finally,the sufficient conditions for the local solution explosive are obtained by using energy inequalities:when p>max {q,p-2},the local solution either explosive with a positive probability in a finite time,or explosive in the sense of energy,where p is a quasilinear index.And obtaining the noise term delays the energy explosion.In the third chapter,we study the initial boundary value problem of stochastic quasilinear evolution equations with memory terms driven by additive noise.We prove the existence of global solution and asymptotic stability of the solution using some properties of the convex functions.The specific results are as follows:When the memory item g'(t)?-cgp(t),1<p<3/2(c>0),the solution energy satisfies E?(t)? k3G-1{k1t+k2);when p=1,the solution energy satisfies E?(t)? k3G-1(k1t+k2)+(M+2c)E1.In the fourth chapter,we have summarized the contents of the research in this article and prospected the future research direction.