Existence And Blow-up Of Solution For Neumann Boundary Value Problem Of Nonlinear Wave Equation With Damping And Source Terms

In this paper, we mainly study the following wave equation with nonlinear damping and source terms.where△is Laplace operator,p,m>1,|ut|m-1ut is the damping term and|u|p-1is the source term.In chapter two, the existence of the weak solutions for this equation with nonlinear Neu-mann boundary value condition (as follows) is proved by Faedo-Galerkin method. More-over, the blowing up conditions of the solution are given.In chapter three, we consider a nonlinear wave equation with damping and source term with nonlinear Neumann boundary value condition(as follows).we show that the solution bolws up in finite time for vanishing initial energy.The criteria to guarantee blow-up of solutions with positive initial energy are established both for linear (m=1) and nonlinear damping case, and global existence of the solution is discussed.