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Asymptotic stablity of invasion fronts for reaction-diffusion equations

Abstract : In several equations such as reaction-diffusion PDE, propagating solutions called fronts, that may model the evolution of a population over time, sometimes appear. To decide which of this solutions are the stable ones is fundamental, since they attract, and thus describe, generic solutions. In this PhD, I study the asymptotic stability of monostable fronts in three distinct and explicit models, each presenting their own characteristics. We will see that the asymptotic stability of monostable fronts remains in the three following cases: when a singular term is added; when a Turing instability arise behind the front; in a hyperbolic case. The approach that is used can be qualified of dynamical, since the main argument uses a Duhamel formulation and a spectral study at linear level.
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https://theses.hal.science/tel-03813672
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Submitted on : Thursday, October 13, 2022 - 2:50:09 PM
Last modification on : Tuesday, October 25, 2022 - 11:58:11 AM

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2022TOU30127a.pdf
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  • HAL Id : tel-03813672, version 1

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Louis Garenaux. Asymptotic stablity of invasion fronts for reaction-diffusion equations. Analysis of PDEs [math.AP]. Université Paul Sabatier - Toulouse III, 2022. English. ⟨NNT : 2022TOU30127⟩. ⟨tel-03813672⟩

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