Correctors for some asymptotic problems

In the theory of anisotropic singular perturbation boundary value problems, the solution u ɛ does not converge, in the H 1-norm on the whole domain, towards some u 0. In this paper we construct correctors to have good approximations of u ɛ in the H 1-norm on the whole domain. Since the anisotropic singular perturbation problems can be connected to the study of the asymptotic behaviour of problems defined in cylindrical domains becoming unbounded in some directions, we transpose our results for such problem

On a class of integro-differential problems

Abstract. The paper is concerned with the existence of solutions to an integrodifferential problem arising in the neutron transport theory. By an anisotropic singular perturbations method we show that solutions of such a problem exist and are close to those of some nonlocal elliptic problem. The existence of the solutions of the nonlocal elliptic problem with bounded data is ensured by the Schauder fixed point theorem. Then an asymptotic method is applied in the general case. The limits of the solutions of the nonlocal elliptic problems are solutions of our integro-differential problem

On some anisotropic, nonlocal, parabolic singular perturbations problems

This paper is devoted to the study of the anisotropic singular perturbations theory for some quasilinear parabolic problems. Describing the asymptotic behaviour of the solutions of nonlocal problems yields to show the existence of solution to some integro-differential problems. The closeness between the solutions of these two kinds of problems is established

Correctors for some asymptotic problems

In the theory of anisotropic singular perturbation boundary value problems, the solution u ɛ does not converge, in the H 1-norm on the whole domain, towards some u 0. In this paper we construct correctors to have good approximations of u ɛ in the H 1-norm on the whole domain. Since the anisotropic singular perturbation problems can be connected to the study of the asymptotic behaviour of problems defined in cylindrical domains becoming unbounded in some directions, we transpose our results for such problems

Asymptotic behavior of elliptic boundary-value problems with some small coefficients

The aim of this paper is to analyze the asymptotic behavior of the solutions to elliptic boundary-value problems where some coefficients become negligible on a cylindrical part of the domain. We show that the dimension of the space can be reduced and find estimates of the rate of convergence. Some applications to elliptic boundary-value problems on domains becoming unbounded are also considered

Etude du comportement asymptotique de certaines équations aux dérivées partielles dans des domaines cylindriques

La recherche dans le domaine des équations aux dérivées partielles s'intéresse d'une part aux propriétés qualitatives des modèles, telles que l'existence et l'unicité de la solution, sa régularité et sa stabilité ..., et d'autre part, à la détermination de solutions approchées obtenues par résolution de modèles plus simples. Le travail qu'on présente dans cette thèse rentre dans ce cadre. Il s'intéresse à l'étude d'un type d'approximation, et à l'évaluation de l'erreur commise par son emploi. Le type d'approximation considéré ici consiste à tenir compte des symétries approximativement satisfaites par le problème étudié, et à comparer la solution de ce problème à celle du problème parfaitement symétrique que l'on peut lui associe. Plus spécifiquement, nous nous intéresserons à des problèmes approximativement invariants par translations arbitraires dans p directions (symétrie cylindrique), et nous comparerons la solution de notre problème à celle d'un problème idéal indépendant des coordonnées associées à ces p directions, Nous montrerons que, sous certaines hypothèses, la solution du problème approximativement symétrique tend vers celle du problème parfaitement symétrique lorsque les déviations s'estompent, et nous évaluerons le taux de convergence de la solution du modèle réel vers celle du modèle idéaliséResearch in the field of partial differentiai equations, is interested on the one hand in the qualitative properties of the models, such as existence and uniqueness of the solution, its regularity and its stability, , . , and on the other hand, in the determination of approximated solutions obtained as solutions of simpler models. The work which we present in this thesis belongs to the second framework. lt considers a , type of approximation and evaluates the error made by its use. The type of approximation considered here consists in taking account of roughly satisfied symmetries, and comparing the solution of this problem with that of the perfectly symmetrical problem which we can associate to it. More specifically, we will be interested in problems invariants by arbitrary translations in p directions (cylindrical symmetry), and we will compare the solution of our problem with that of an ideal problem independent of the co-ordinates associated with thesE p directions, We will show that, under certain assumptions, the solution of the roughly symmetrical problem tends towards the solution of the perfectly symmetrical problem when the deviations decrease, and we will evaluate the rate of convergence of the solution of the real madel towards the solution of the idealized madel.MULHOUSE-SCD Sciences (682242102) / SudocSudocFranceF

On some anisotropic, nonlocal, parabolic singular perturbations problems

This article is devoted to the study of the anisotropic singular perturbations theory for some quasilinear parabolic problems. Describing the asymptotic behaviour of the solutions of nonlocal problems yields to show the existence of solution to some integro-differential problems. The closeness between the solutions of these two kinds of problems is established

Existence of solutions and iterative approximations for nonlinear systems arising in free convection

We study the existence and the regularity of the solutions of some nonlinear partial differential system arising in the study of free convection in a two-dimensional bounded domain, modeling a porous medium saturated with a fluid. By introducing an iterative method, the closeness of such solutions by solution of linear elliptic problems is given with an exponential rate of convergence