The Blow-up Behaviors Of Solutions To Some Nonlinear Wave Equations

At present,the nonlinear wave equation is a typical nonlinear evolution equation which is of importance theoretical significance and application value.It is a very active topic in the field of partial differential equations,and has been highly studied by domestic and foreign scholars.We consider the blow-up behaviors of the solutions of the initial boundary value problem for some nonlinear wave equations.The specific forms are listed as follows:(?)(?)(?)(?)(?)(?)There are five chapters in this thesis:In chapter 1,we state the research background and status of nonlinear wave equations,and the main contents of this paper.In chapter 2,using the potential theory,we construct the instability set and apply the convexity analysis method to prove the initial-boundary value problem of the nonlinear fourth-order wave equation.When the initial energy is positive,but there is an appropriate upper bound,the solution of the equation will blow up at a finite time in the sense of the L2(Ω)norm;using the eigenfunction method,the nonlinearity is proved for the initial boundary value problem of the fourth-order wave equation,when the nonlinear term and initial value satisfy certain conditions,the smooth solution tends to infinity in finite time.In chapter 3,using the eigenfunction method,we prove the problem of the initial bound-ary value of the strongly damped nonlinear wave equation.When the nonlinear term and the initial value satisfy certain conditions,the smooth solution is Limited time tends to infinity.In chapter 4,using the eigenfunction method,we prove the initial boundary value prob-lems of the nonlinear wave equation with integral differential terms.When the nonlinear term and initial value satisfy certain conditions,smooth solutions tend to infinity in finite time.Chapter 5 summarizes the full text and presents perspectives.