| Titre : | Etude Qualitative studies of some dissipative systems for wave equation |
| Auteurs : | Derradji Guidad, Auteur ; ZENNI Khaled, Directeur de thèse ; Mohamed Berbiche, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2022 |
| Format : | 1 vol. (106 p.) / couv. ill. en coul / 30 cm |
| Langues: | Français |
| Mots-clés: | Viscoelastic wave equation, Strong nonlinear system, Global solution, Faedo-Galerkin approximation, Decay rate, Blow up, Strong damping, Distributed delay, Porous-elastic system. |
| Résumé : |
The present thesis is devoted to the study of well-posedness and asymptotic behaviour in time of solution for damped systems. This work consists of four chapters. In chapter 1, we recall of some fundamental inequalities. In chapter 2, we consider a very important problem from the point of view of application in sciences and engineering. A system of three wave equations having a different damping effects in an unbounded domain with strong external forces. Using the FaedoGalerkin method and some energyestimates, we will prove the existence of global solution in R nowing to to the weighted function. By imposing a new appropriate conditions, which are not used in the literature, with the help of some special estimates and generalized Poincar´e’s inequality, we obtain an unusual decay rate for the energy function. In chapter 3, we will concerned witha problem for coupled nonlinear viscoelastic wave equation with distributed delay and strong damping and source terms, under suitable conditions we prove a blow up/growth results of solutions. In chapter 4, we consider one-dimensional porous-elastic system with nonlinear damping, infinite memory and distributed delay terms. We show the well posedness of solution by the semigroup theory and that the solution energy has an explicit and optimal decay, for the cases of equal and nonequal speeds of wave propagation. |
| Sommaire : |
Introduction 8 1 Preliminary 14 1.1 Continuous function spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2 L p Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3 Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.1 W1,p (Ω) spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.2 W m,p (Ω) Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Semigroups of bounded linear operators . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5 Lyapunov Stability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.5.1 Notations and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.5.2 Lyapunov type stability theorem . . . . . . . . . . . . . . . . . . . . . . . 25 1.5.3 Procedure of Lyapunov functionals construction . . . . . . . . . . . . . . . 26 1.6 Problems with a delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2 The effect of damping terms on decay rate for system of three nonlinear wave equations with memories 33 2.1 Position of problem and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2 Main results and Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3 Coupled nonlinear viscoelastic wave equation with distributed delay and strong damping and source terms 48 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2 Blow up in finite time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3 Growth of solutions to system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4 Well-posedness and stability result for a nonlinear damped porous-elastic system with infinite memory and distributed delay terms 70 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.2 Well-posedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3 Stability Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 |
| En ligne : | http://thesis.univ-biskra.dz/5689/1/THESE%20GUIDAD%20DERRADJI.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/121 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
