The Study Of Solution For A Type Of Evolution Equations

In this paper, we study the existence of the global solution, the Blow-up and the traveling wave solution for the generalized D-P type equation and the generalized hyperlastic-rod wave equation. There are there sections in this paper.The first sections, we introduce the background and actuality and summarize the main result.The second sections, we consider the initial boundary value problem of the generalized D-P type equation on half line and bounded interval, with Kato's method for abstract quasi-linear evolution equations and a prior estimates of solution, we get the existence of the global solution and the Blow-up of solution in finite time under some conditions.Finally, we consider the initial boundary value problem of the generalized hyperlastic-rod wave equation on half line and bounded interval, by the methods of prior estimates, the existence of the global solution are proved. By discuss limiting zero point of the equation, some sufficient condition that guarantee the existence and uniqueness of traveling wave solution of this equation are obtained.