Blow-up Results For The Wave Equations

Boundary conditions effect the solution to the wave equation.A nonlinear wave equationwas concerned.The solution global exists,and blows up in a finite time. This paper was concerned with a one-dimensional linear wave equation associated with nonlinear boundary conditions.A unique local solution to the wave equation was proved to existThe result is that the nonlinearity at the boundary causes a finite time blow up of the solution,even for small initial data.And the upper bound to the blow up time is given in the paper.This dissertation contains three chapters: In Chapter 1 we introduce some background knowledge of the solution to the wave equation. In Chapter 2 we study the solution to the nonlinear wave equation.In Chapter 3 we study the solution to the linear wave equation.