# Equations de réaction-diffusion de type KPP : ondes pulsatoires, dynamique non triviale et applications.

Abstract : In this thesis, we study reaction-diffusion equations of KPP (Kolmogorov, Petrovsky and Piskunov) type in periodic media. These equations arise in the modelling of combustion and ecology.
We are especially interested on pulsating waves and solutions close to them as well as their qualitative properties. The main part of our work is devoted to an equation of KPP type in unidimensional periodic media $u_t - u_{xx}=f(x,u)$. We prove first existence of pulsating waves with precise behaviour at infinity, then we exhibit nontrivial large time dynamics. Finally, we study the SHS (Self-propagating High-temperature Synthesis) reaction diffusion system of solid combustion, for which we show existence of pulsating waves with an half line of admissible speeds.
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https://tel.archives-ouvertes.fr/tel-00262323
Contributor : Michaël Bages <>
Submitted on : Tuesday, March 11, 2008 - 2:23:17 PM
Last modification on : Thursday, March 5, 2020 - 5:57:10 PM
Long-term archiving on: : Friday, May 21, 2010 - 12:10:37 AM

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• HAL Id : tel-00262323, version 1

### Citation

Michaël Bages. Equations de réaction-diffusion de type KPP : ondes pulsatoires, dynamique non triviale et applications.. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2007. Français. ⟨tel-00262323⟩

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