Département de mathématique

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Comportement de la solution de certains systèmes d'évolution semi linéaire
(2023) ABDELHADI SOUMIA
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.