Bolw-up Of Solutions Of Initial Boundary Value Problem For A Class Of Nonlinear Klein-Gordon Equation

In this paper, the blowing up behavior of the solution for a class of nonlinear Klein-Gordon equation is studied. As the first step, the usage of the important theorem of the Sobolev space (embedding theorem) supplies some exciting conclusions by discussion of the method of protruding analysis and the function of energy with the positive and negative cases being considered. When the initial energy is negative the problem discussed will blow up by choosing the appropriate initial value; On the other hand, if the initial energy has upper bound, the problem concerned will blow up when the initial energy is positive. And this upper bound ties up with the Sobolev embedding constant of the considered space exclusively.Moreover, this paper researches an interesting problem-whe -ther or not the nonlinear term affects the blowing up of the problem discussed. By introducing the "blowing up factor" , we get new results. Under the two different boundary conditions of Neuman and Dirichlet, the problem discussed will blow up when it satisfies some conditions which tying up with the nonlinear term.As a result, we can estimate whether the physical model or the mathematical model correspondingly has warp or not when the blow up of the solution is known.