DIFFERENTIAL EQUATIONS IN CYLINDRICAL DOMAINS"

Abstract

Research in the field of partial differential 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. It 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 him. More specifically, we will be interested in problems invariants by translations arbitrary 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 that of the perfectly symmetrical problem when the deviations decrease, and we will evaluate the rate of onvergence of the solution of the real model towards that of the idealized model.

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