Qualitative study of some dissipative systems for partial differential equations of hyperbolic-type.

Abstract

In this thesis, we study the existence/nonexistence in time as well as the asymptotic behavior of some viscoelastic problems in the presence of different damping and different nonlinearities in the sources. In this regard, we prove several decay results under appropriate assumptions on the kernels and the structural parameters of the equations. We use the multiplier method, the well depth method to establish the desired stability results of the problems. Our results generalize many results existing in the literature.