Some problems of direct and indirect stabilization of wave equations with locally boundary fractional damping or with localised Kelvin-Voigh

Abstract : This thesis is devoted to study the stabilization of the system of waves equations with one boundary fractional damping acting on apart of the boundary of the domain and the stabilization of a system of waves equations with locally viscoelastic damping of Kelvin-Voight type. First, we study the stability of the multidimensional wave equation with boundary fractional damping acting on a part of the boundary of the domain. Second, we study the stability of the system of coupled onedimensional wave equation with one fractional damping acting on a part of the boundary of the domain. Next, we study the stability of the system of coupled multi-dimensional wave equation with one fractional damping acting on a part of the boundary of the domain. Finally, we study the stability of the multidimensional waves equations with locally viscoelastic damping of Kelvin-Voight is applied for one equation around the boundary of the domain.
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Mohammad Akil. Some problems of direct and indirect stabilization of wave equations with locally boundary fractional damping or with localised Kelvin-Voigh. Analysis of PDEs [math.AP]. Université de Limoges, 2017. English. ⟨NNT : 2017LIMO0043⟩. ⟨tel-01619455⟩

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