EXISTENCE DE LA SOLUTION DE CERTAINS SYSTEMES D’EVOLUTION SEMI LINEAIRE. Doctorat thesis (2019), Université de Batna 2.

Abstract

The main objective of this thesis is to study the problem of the global existence and stability of some semi linear evolution systems. The first study focuses on the nonlinear hyperbolic equation with damping and source terms. To prove the existence of a global solution of this system, we use some assumptions for initial data. Then, by applying an integral inequality due to Komornik, we obtain the stability result. The second study highlights the nonlinear wave equation with damping and source terms of variable-exponent types. Also, by some assumptions for initial data and Komornik’s integral inequality, we obtained similar results. Finally, we consider the nonlinear wave equation with damping, source and nonlinear first order perturbation terms. We show that when the damping term (linear and viscoelastic) dominates the nonlinear first order perturbation terms, the usual energy is decreases and the solution is global.