Etude de quelques problèmes aux limites hyperboliques semi linéaires : existence locale et globale, comportement asymptotique et explosion en temps fini des solutions

Abstract

In this work, we consider two semi linear hyperbolic problems with polynomial source term; the first is a semi linear problem with nonlinear dissipative term for a strongly elliptic operator with variable coefficients. However, the second problem is concerned to the viscoelastic wave equations with variable coefficients and acoustic boundary conditions. Under some hypothesis on the initial data by using a recently results in mathematical analysis, then important results on local and global existence, uniqueness, asymptotic decay and below up in finite time of solutions are given.