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Etude de l'existence et de la stabilité de dynamiques explosives pour des problèmes paraboliques critiques.

Abstract : In this thesis, we have obtained a sharp description of blow-up dynamics (Universality of the bubble and the speed of the concentration, stability of the formation of the singularity) for three critical parabolic problems : harmonic heat flow in dimension two for the 1-corotational solutions, the energy critical semilinear heat flow in dimension four and the Patlak-Keller-Segel model in the parabolic-elliptic version, for supercritical mass solutions (M>8π). The first four chapters are devoted to the presentation of each problem, as well as the strategy of the proof. In the last three chapters have been placed submitted articles.
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https://theses.hal.science/tel-00969133
Contributor : Rémi Schweyer Connect in order to contact the contributor
Submitted on : Wednesday, April 2, 2014 - 10:24:00 AM
Last modification on : Friday, August 5, 2022 - 2:46:00 PM
Long-term archiving on: : Wednesday, July 2, 2014 - 11:30:15 AM

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  • HAL Id : tel-00969133, version 1

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Rémi Schweyer. Etude de l'existence et de la stabilité de dynamiques explosives pour des problèmes paraboliques critiques.. Equations aux dérivées partielles [math.AP]. Université Paul Sabatier - Toulouse III, 2013. Français. ⟨NNT : ⟩. ⟨tel-00969133⟩

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