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2020 Propagation properties of reaction-diffusion equations in periodic domains
Romain Ducasse
Anal. PDE 13(8): 2259-2288 (2020). DOI: 10.2140/apde.2020.13.2259

Abstract

We study the phenomenon of invasion for heterogeneous reaction-diffusion equations in periodic domains with monostable and combustion reaction terms. We give an answer to a question raised by Berestycki, Hamel and Nadirashvili concerning the connection between the speed of invasion and the critical speed of fronts. To do so, we extend the classical Freidlin–Gärtner formula to such equations and we derive some bounds on the speed of invasion using estimates on the heat kernel. We also give geometric conditions on the domain that ensure that the spreading occurs at the critical speed of fronts.

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Romain Ducasse. "Propagation properties of reaction-diffusion equations in periodic domains." Anal. PDE 13 (8) 2259 - 2288, 2020. https://doi.org/10.2140/apde.2020.13.2259

Information

Received: 16 April 2018; Revised: 4 July 2019; Accepted: 7 October 2019; Published: 2020
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.2140/apde.2020.13.2259

Subjects:
Primary: 35B06, 35B40, 35B51, 35K05, 35K57

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 8 • 2020
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