Existence and asymptotic behavior for some hyperbolic systems

RAHMOUNE, Abdelaziz (2018) Existence and asymptotic behavior for some hyperbolic systems. Doctoral thesis, MOHAMED KHIDER UNIVERSITY, BISKRA.


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This thesis is devoted to study the Existence and asymptotic behavior for some hyperbolic systems . The first part of the thesis is composed of two chapters 2 and 3. We studied a one-dimensional linear thermoelastic system of Timoshenko type, where the heat flux is given by Cattaneo’s law, noting that in the chapter 3 we have introduced a delay term in the feedback and forcing term. We established several exponential decay results for classical and weak solutions in one-dimensional. Our technics of proof is based on the construction of the appropriate Lyapunov function equivalent to the energy of the considered solution, and which satisfies a di�erential inequality leading to the desired decay. In chapter 4, we consider a system of nonlinear wave equation with degenerate damping and strong nonlinear source terms. We prove that the solution blows up in time.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: Nonlinear damping, Strong damping, Viscoelasticity, Nonlinear source, Locale solutions, Global solution, Exponential decay, Polynomial decay, Blow up.
Subjects: Q Science > QA Mathematics
Divisions: Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie > Département de Mathématiques
Depositing User: BFSE
Date Deposited: 06 Jan 2019 08:24
Last Modified: 06 Jan 2019 08:24
URI: http://thesis.univ-biskra.dz/id/eprint/3843

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