Propagation properties of reaction-diffusion equations in periodic domains

Ducasse, Romain

doi:10.2140/apde.2020.13.2259

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1948-206X (e-only)

ISSN: 2157-5045 (print)

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

Propagation properties of reaction-diffusion equations in periodic domains

Romain Ducasse

Vol. 13 (2020), No. 8, 2259–2288

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.

PDF Access Denied

We have not been able to recognize your IP address 3.139.107.241 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

propagation, spreading, reaction-diffusion equations, heat kernel, domains with obstacles, periodic domains, parabolic equations, elliptic equations, speed of propagation, geometry of the domain

Mathematical Subject Classification

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

Milestones

Received: 16 April 2018

Revised: 4 July 2019

Accepted: 7 October 2019

Published: 28 December 2020

Authors

Romain Ducasse
École des Hautes Études en Sciences Sociales PSL Research University Centre d’Analyse et Mathématiques Sociales Paris, France

Vol. 13, No. 8, 2020