Comportement de la solution de certains systèmes d'évolution semi linéaire
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Date
2023
Authors
ABDELHADI SOUMIA
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Abstract
In the first part of this work, we consider a nonlinear hyperbolic equation with variable
damping and source terms. Our aim is to prove that the solution with negative initial energy
blows up in finite time. After that, we consider a coupled system of nonlinear wave equations
with variable exponents in the damping terms. By using the multiplier method, we prove the
decay estimates for the solution under appropriate assumptions on these exponents. In the
third part, we study the wave equation with damping, source and nonlinear first order
perturbation terms. Our aim is to prove that if the damping terms dominated the first order
perturbation term then the energy is decreasing and the solutions with sufficiently negative
initial energy blow up in finite time.