Aiachi , MarwaOUAOUA , Amar2025-01-062025-01-062024http://dspace.univ-skikda.dz:4000/handle/123456789/3702In this memory, we study two problems: the first concerns a quasi-linear parabolic system with a weak visco-elastic term, and the second concerns the wave equation. In the first problem, we proved the existence of a global solution in a bounded domain with homogeneous Dirichlet conditions. We also proved that this solution decays exponentially, meaning that as time approaches to infinity, the solution approaches to zero. Second, we proved that the solution to the wave equation, also under homogeneous Dirichlet conditions, blows up in finite time. The study is based on Nehari space.enMasters degree Thesis