Existence and nonexistence of global solutions for nonlinear transmission acoustic problem

Abstract

In this paper we consider a mixed problem for the nonlinear wave equations with transmission acousticconditions, that is, the wave propagation over bodies consisting of two physically different types of materials, one ofwhich is clamped. We prove the existence of a global solution. Under the condition of positive initial energy we showthat the solution for this problem blows up in finite time.