ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A PARTIAL DIFFERENTIAL EQUATION
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Date
2024
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Publisher
Faculty of Sciences
Abstract
In 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.