Blow Up Of Solutions Of A Nonlinear Viscoelastic Wave Equation In R~N

Wave equation is an important research content of the theory of partial differential equations, the study of it will promote the theory of partial differential equations and the further development of other branches of mathematics. In this work, using convex analysis method and energy method, studied blow up of the two nonlinear viscoelastic wave equations. The research of this work detailed below.Firstly, We introduce the background and overview of issues related to development and the main content and structure of this work.Secondly, given the prior knowledge to solve the problem, a list of theorems and inequalities to prove the main results.The last, on the basis of predecessors’research, though finite propagation of the wave, proves that the non-linear damping viscoelastic wave equation and a tiny distur-bance which was added to this equation and the formation of a new equation of solution of blow up in the region of the unbounded, respectively.