Skip to Main content Skip to Navigation
Theses

Formules de monotonie appliquées à des problèmes à frontière libre et de modélisation en biologie

Abstract : This thesis presents regularity results for partial differential equations of parabolic type. In the first part we concentrate on free boundary problems which stem from the parabolic obstacle problem with variable
coefficients. We prove regularity results for the solution and for the free boundary. This study uses blow-up and monotonicity formulae methods. The second part is dedicated to a problem which comes from aggregation modelling in biology: the
Keller-Segel system. Making use of a free energy, we prove the existence of a threshold which governs the initial data, below which the solutions exist, and above which they blow-up in finite time. We specify their long-time behaviour in the case where the solutions exist.
Document type :
Theses
Complete list of metadatas

Cited literature [210 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00011381
Contributor : Adrien Blanchet <>
Submitted on : Friday, January 13, 2006 - 10:10:23 PM
Last modification on : Wednesday, September 23, 2020 - 4:27:31 AM
Long-term archiving on: : Saturday, April 3, 2010 - 9:23:27 PM

Identifiers

  • HAL Id : tel-00011381, version 1

Collections

Citation

Adrien Blanchet. Formules de monotonie appliquées à des problèmes à frontière libre et de modélisation en biologie. Mathématiques [math]. Université Paris Dauphine - Paris IX, 2005. Français. ⟨tel-00011381⟩

Share

Metrics

Record views

270

Files downloads

750