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A simple flattening lower bound for solutions to some linear integrodifferential equations

Coville, Jérôme; Bouin, Emeric; Legendre, Guillaume (2023), A simple flattening lower bound for solutions to some linear integrodifferential equations. https://basepub.dauphine.psl.eu/handle/123456789/24509

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Type
Document de travail / Working paper
Date
2023
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
7
Metadata
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Author(s)
Coville, Jérôme cc
Biostatistique et Processus Spatiaux [BioSP]
Bouin, Emeric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Legendre, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Estimates on the asymptotic behaviour of solution to linear integro-differential equations are fundamental in understanding the dynamics occuring in many nonlocal evolution problems. They are usually derived by using precise decay estimates on the heat kernel of the considered diffusion process. In this note, we show that for some generic jump diffusion and particular initial data, one can derive a lower bound of the asymptotic behaviour of the solution using a simple PDE argument. This is viewed as an independant preliminary brick to study invasion phenomena in nonlinear reaction diffusion problems.
Subjects / Keywords
integro-differential operators; fractional Laplace operator; acceleration; spreading