The asymptotic behavior of some hyperbolic PDE systems / Hizia Bounadja  

Public ISBD Titre : The asymptotic behavior of some hyperbolic PDE systems Type de document : texte imprimé Auteurs : Hizia Bounadja, Auteur ; Belkacem Said-houari, Directeur de thèse Année de publication : 2022 Importance : 1 vol (127 f .) Format : 29 cm Langues : Français (fre) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Moore-Gibson-Thompson equation Memory kernel Index. décimale : 515- mathèmatique Résumé : The main goal of this dissertation is to discuss the asymptotic behavior of some hyperbolic PDE systems, precisely, we handled the well-posedness and stability of the solutions for the Moore-Gibson-Thompson equation (MGT) employing various types of dissipation. In fact, under an appropriate assumption on the coefficients of the systems together with the energy method in Fourier space we have proved the well-posedness of the systems and built some Lyapunov functionals which allowed us to get control estimates on the Fourier image of the solution and led to the decay rate of the L2-norm of the solution. On the other hand, by comparing the behavior of the resolvent of the Moore-Gibson-Thompson system with the one of the resolvent of the wave equation with a frictional interior damping, we furnish weaker conditions that guarantee exponential, polynomial or even logarithmic decay of the solution of the Moore-Gibson-Thompson system in a bounded domain. Côte titre : MD/0168 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/3929/1/Hizia_Thesis_2 [...] Format de la ressource électronique : PDF The asymptotic behavior of some hyperbolic PDE systems [texte imprimé] / Hizia Bounadja, Auteur ; Belkacem Said-houari, Directeur de thèse . - 2022 . - 1 vol (127 f .) ; 29 cm. Langues : Français (fre) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Moore-Gibson-Thompson equation Memory kernel Index. décimale : 515- mathèmatique Résumé : The main goal of this dissertation is to discuss the asymptotic behavior of some hyperbolic PDE systems, precisely, we handled the well-posedness and stability of the solutions for the Moore-Gibson-Thompson equation (MGT) employing various types of dissipation. In fact, under an appropriate assumption on the coefficients of the systems together with the energy method in Fourier space we have proved the well-posedness of the systems and built some Lyapunov functionals which allowed us to get control estimates on the Fourier image of the solution and led to the decay rate of the L2-norm of the solution. On the other hand, by comparing the behavior of the resolvent of the Moore-Gibson-Thompson system with the one of the resolvent of the wave equation with a frictional interior damping, we furnish weaker conditions that guarantee exponential, polynomial or even logarithmic decay of the solution of the Moore-Gibson-Thompson system in a bounded domain. Côte titre : MD/0168 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/3929/1/Hizia_Thesis_2 [...] Format de la ressource électronique : PDF

Exemplaires (1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
DM/0168	DM/0168	Thèse	Bibliothéque des sciences	Anglais	Disponible Disponible

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