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Melle<\/sup><\/span>\u00a0BENAOUDIA Djamila.<\/span><\/strong><\/p>\n Soutiendra sa th\u00e8<\/em>se de Doctorat en Es-Science en Math\u00e9matiques Sp\u00e9cialit\u00e9: Analyse.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/p>\n Intitul\u00e9:\u00a0\u00ab<\/strong>On the asymptotic behaviour of some singular perturbations problems<\/span> <\/strong>\u00bb<\/span><\/p>\n Le\u00a0:<\/span> 06 Juillet 2022 <\/span><\/strong>\u00e0 la salle de visioconf\u00e9rences du Centre des Syst\u00e8mes et R\u00e9seaux de l\u2019Universit\u00e9 \u00a0Mouloud Mammeri de Tizi-Ouzou \u00e0<\/span> 9h :00.<\/strong><\/span><\/p>\n Directrice de Th\u00e8se\u00a0: Pr BEDOUHENE Fazia<\/span><\/strong><\/p>\n <\/strong><\/span><\/p>\n Devant le jury compos\u00e9 de :<\/strong><\/span><\/p>\n <\/strong><\/p>\n <\/strong><\/span><\/p>\n R\u00e9sum\u00e9:<\/strong><\/span><\/p>\n Notre travail consiste \u00e0 \u00e9tudier un probl\u00e8me du type int\u00e9gro-diff\u00e9rentiel qui d\u00e9coule de la th\u00e9orie de transport des neutrons en introduisant un type de probl\u00e8mes appel\u00e9s probl\u00e8mes perturb\u00e9s. L\u2019\u00e9tude des probl\u00e8mes de perturbations singuli\u00e8res occupe une place importante parmi les probl\u00e8mes math\u00e9matiques \u00e9tudi\u00e9s de nos jours et dans le pass\u00e9. En effet, ce type des probl\u00e8mes se pr\u00e9sente souvent dans la nature, ils sont caract\u00e9ris\u00e9s par la pr\u00e9sence d\u2019un petit param\u00e8tre qui lorsqu\u2019il tend vers z\u00e9ro, donne lieu g\u00e9n\u00e9ralement \u00e0 un ph\u00e9nom\u00e8ne physique appel\u00e9 \u00ab\u00a0couches limites\u00a0\u00bb. Dans les \u00e9tudes th\u00e9oriques, ces probl\u00e8mes apparaissent de deux fa\u00e7ons diff\u00e9rentes: Soit physiquement, le petit param\u00e8tre \u00e9tant une donn\u00e9e du probl\u00e8me, par exemple un coefficient de diffusion, ou un coefficient de viscosit\u00e9, etc…, et dans ce cas on cherche \u00e0 comparer la solution de ce probl\u00e8me \u00e0 celle du probl\u00e8me limite qui correspond (au moins formellement) \u00e0 la valeur nulle de ce param\u00e8tre. Soit inversement, les perturbations singuli\u00e8res peuvent apparaitre indirectement comme un outil de d\u00e9monstration; ce sont les m\u00e9thodes dites de \u00ab\u00a0r\u00e9gularisation\u00a0\u00bb ou de \u00ab\u00a0viscosit\u00e9 artificielle\u00a0\u00bb qui consistent \u00e0 renforcer la r\u00e9gularit\u00e9 de l\u2019\u00e9quation en ajoutant un terme plus r\u00e9gulier affect\u00e9 d\u2019un petit coefficient. Le travail de recherche effectu\u00e9 dans ma th\u00e8se vise \u00e0 \u00e9tudier des \u00e9quations int\u00e9gro-diff\u00e9rentielles non-lin\u00e9aires soumises \u00e0 des conditions aux limites du type Dirichlet homog\u00e8nes. Nous \u00e9tablissons l\u2019existence de solutions en employant la m\u00e9thode des perturbations singuli\u00e8res comme outil naturel. Les probl\u00e8mes perturb\u00e9s sont des probl\u00e8mes hyperboliques classiques, non locaux, non-lin\u00e9aires et les limites des sous-suites de leurs solutions, dans des espaces de type Sobolev, sont des solutions du probl\u00e8me principal.<\/span><\/p>\n Mots cl\u00e9s<\/strong><\/span>\u00a0: Probl\u00e8me int\u00e9gro-diff\u00e9rentiel, perturbations singuli\u00e8res anisotropes, probl\u00e8mes hyperboliques, transport des neutrons.<\/p>\n \u00a0Abstract:<\/strong><\/span><\/p>\n Our work consists in studying a problem of the integro-differential type which derives from the theory of neutron transport by introducing a type of problem called perturbed problems. The study of singular perturbations problems occupies an important place among the mathematical problems studied today and in the past. Indeed, this type of problem often occurs in nature, they are characterized by the presence of a small parameter which when it tends towards zero, generally gives rise to a physical phenomenon called \u00ab\u00a0boundary layer\u00a0\u00bb. In theoretical studies, these problems appear in two different ways: Either physically, the small parameter being a given of the problem, for example a coefficient of diffusion, or a coefficient of viscosity, etc …, and in this case one seeks to compare the solution of this problem with that of the limit problem which corresponds (at least formally) to the null value of this parameter. Or conversely, the singular perturbations can appear indirectly as a demonstration tool; these are the so-called\u00a0 \u00ab\u00a0regularization\u00a0\u00bb or \u00ab\u00a0artificial viscosity\u00a0\u00bb methods which consist in reinforcing the regularity of the equation by adding a more regular term affected by a small coeffcient. The research work carried out in my thesis aims to study nonlinear integro-differential equations subjected to homogeneous Dirichlet-type boundary conditions. We establish the existence of solutions using the method of singular perturbations as a natural tool. The perturbed problems are classical hyperbolic, nonlocal, nonlinear problems and the limits of the subsequences of their solutions, in Sobolev-type spaces, are solutions of the main problem.<\/p>\n \u00a0Keywords\u00a0<\/strong>:<\/span> Integro-differential problems, anisotropic singular perturbations, hyperbolic problems, neutron transport.<\/p>\n \u00a0<\/span><\/p>\n \u00a0<\/span><\/p>\n \u00a0<\/span><\/p>\n \u00a0<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":" Melle\u00a0BENAOUDIA Djamila. Soutiendra sa th\u00e8se de Doctorat en Es-Science en Math\u00e9matiques Sp\u00e9cialit\u00e9: Analyse.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 Intitul\u00e9:\u00a0\u00abOn the asymptotic behaviour of some singular perturbations problems \u00bb Le\u00a0: 06 Juillet 2022 \u00e0 la salle de visioconf\u00e9rences du Centre des Syst\u00e8mes et R\u00e9seaux de l\u2019Universit\u00e9 \u00a0Mouloud Mammeri de […]<\/p>\n","protected":false},"author":13,"featured_media":6032,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-14267","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-non-classe"],"yoast_head":"\n\n\n
\n Mme RAHMANI Leila<\/strong><\/strong><\/td>\n Professeure<\/strong><\/td>\n UMMTO<\/strong><\/td>\n Pr\u00e9sidente<\/strong><\/td>\n<\/tr>\n \n Mme BEDOUHENE Fazia<\/strong><\/td>\n Professeure<\/strong><\/td>\n UMMTO<\/strong><\/td>\n Directrice de th\u00e8<\/em>se<\/strong><\/td>\n<\/tr>\n \n Mr. MOULAY Mohamed Said<\/strong><\/td>\n Professeur<\/strong><\/td>\n USTHB<\/strong><\/td>\n Examinateur<\/strong><\/td>\n<\/tr>\n \n Mr.SENGOUGA Abdelmouhcene<\/strong><\/td>\n MCA<\/strong><\/td>\n Universit\u00e9 de \u00a0M\u2019sila<\/strong><\/td>\n Examinateur<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n