Problèmes elliptiques à données peu régulières, applications

Abstract : This document contains works about two main axes of research.

The first one concerns boundary stabilization of some distributed systems in presence of singularities. We are mainly interested in waves equation and elastodynamic system. These problems have been addressed by many authors who have obtained stabilization results by means of multiplier method under restrictive geometric assumptions. In order to extend these results, we have to prove some hidden regularity'' properties concerning strong solutions.
To this end, singularities of some mixed elliptic problems must be analyzed. The knowledge of these singularities allows to generalize a Rellich identity which is crucial to get energy estimates involving stabilization results.

The second axis is devoted to the study of Hele-Shaw flows with a punctual source. Stokes-Leibenson formulation gives an elliptic equation where right hand side is the Dirac distribution. Furthermore this problem is non linear since the domain itself has an unknown behavior. The problem is reformulated by using Helmholtz-Kirchhoff method and this gives a local result of existence and uniqueness of a classical solution. Then a numerical model, so called quasi-contour model'', is built in order to get some qualitative properties of these flows.
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Cited literature [84 references]

https://tel.archives-ouvertes.fr/tel-00002062
Contributor : Jean-Pierre Loheac <>
Submitted on : Tuesday, December 3, 2002 - 11:24:50 AM
Last modification on : Wednesday, July 8, 2020 - 12:42:05 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 6:45:29 PM

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• HAL Id : tel-00002062, version 1

Citation

Jean-Pierre Loheac. Problèmes elliptiques à données peu régulières, applications. Mathématiques [math]. Université Claude Bernard - Lyon I, 2002. ⟨tel-00002062⟩

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