Existence of the solution and stability of an evolution problem
Existence of the solution and stability of an evolution problem
| dc.contributor.author | ALLALI Mohammed | |
| dc.date.accessioned | 2025-09-24T08:21:16Z | |
| dc.date.available | 2025-09-24T08:21:16Z | |
| dc.date.issued | 2025-09-15 | |
| dc.description.abstract | This thesis is focus to studying the nonlinear Korteweg-de Vries equation with internal feedback without delay, also the boundary feedback with either constant or time-dependent delay. We prove the well-posedness of the system and establish the exponential stability of the equation using Lyapunov functional, under certain assumptions like the spatial domain length,also feedback mechanisms, and time-dependent delay. Also, we study the Korteweg-de Vries equation with internal time-varying delay feedback, by proving the exponential stability of the system using an appropriate Lyapunov functional without any assumptions on length of the spatial domain. Finally, we present numerical simulations to illustrate the obtained stability results. | |
| dc.format | ||
| dc.identifier.uri | https://dspace.univ-oran1.dz/handle/123456789/4694 | |
| dc.language.iso | en | |
| dc.publisher | Université Oran 1 | |
| dc.subject | Korteweg-de Vries equation; damping term; amplitude of the wave; boundary feedback with delay; semigroups theory; existence of the solution; energy; exponential stability; Lyapunov functional; nonlinear evolution equation. | |
| dc.title | Existence of the solution and stability of an evolution problem | |
| dc.type | Thesis | |
| grade.Examinateur | BelaibLekhmissi, Professeur, Université Oran 1 | |
| grade.Examinateur | MEZEGHRANI Fatima Zohra, Professeur, Université Oran 1 | |
| grade.Examinateur | HAKEM Ali, Professeur, Université de sidi belabbes | |
| grade.Examinateur | BENAHMED Sfya, Professeur, Ecole Nationale Polytechnique d’Oran | |
| grade.Grade | Doctorat 3éme cycle | |
| grade.Invite | BELGHABA Kacem, Professeur (En retraite), Université Oran 1 | |
| grade.Option | Analyse Mathématique | |
| grade.Président | BOUDAOUD Fatima, Professeur, Université Oran 1 | |
| grade.Rapporteur | Timimoun Chahnaz Zakia, MCA, Université Oran 1 | |
| l'article.1.DateParution | Mai 2025 | |
| l'article.1.Revue | Mathematica | |
| l'article.1.Référence | Volume 67 (90), 41-55, (2025) | |
| l'article.1.Titre | Stability of the KdV equation in the case of mixed internal and boundary dampings with time-dependent delay | |
| la.Mention | Très Honorables | |
| la.Spécialité | Mathématiques | |
| la.cote | TH5616 |
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