Étude des équations des milieux poreux et des modèles de cloques

Abstract : In this thesis, we study two completely independent problems. The first one focuses on a simple mathematical model of thin films delamination and blistering analysis. In the second one, we are interested in the study of the porous medium equation motivated by seawater intrusion problems. In the first part of this work, we consider a simple one-dimensional variational model, describing the delamination of thin films under cooling. We characterize the global minimizers, which correspond to films of three possible types : non delaminated, partially delaminated (called blisters), or fully delaminated. Two parameters play an important role : the length of the film and the cooling parameter. In the phase plane of those two parameters, we classify all the minimizers. As a consequence of our analysis, we identify explicitly the smallest possible blisters for this model. In the second part, we answer a long standing open question about the existence of new contractions for porous medium type equations. For m>0, we consider nonnegative solutions U(t,x) of the following equationU_t=Delta U^m.For 0
Document type :
Theses
Complete list of metadatas

Cited literature [64 references]  Display  Hide  Download

https://pastel.archives-ouvertes.fr/tel-01127042
Contributor : Abes Star <>
Submitted on : Friday, March 6, 2015 - 11:36:15 PM
Last modification on : Tuesday, December 12, 2017 - 3:16:55 AM
Long-term archiving on : Sunday, June 7, 2015 - 9:15:37 PM

File

2014PEST1080.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01127042, version 1

Collections

Citation

Ghada Chmaycem. Étude des équations des milieux poreux et des modèles de cloques. Mathématiques générales [math.GM]. Université Paris-Est, 2014. Français. ⟨NNT : 2014PEST1080⟩. ⟨tel-01127042⟩

Share

Metrics

Record views

368

Files downloads

379