Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation

Gregoire Nadin; Benoit Perthame; Min Tang

hal-00537986, version 1

Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation

Gregoire Nadin ¹, Benoit Perthame ^1, 2, Min Tang () ²

Abstract: This note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in \cite{BNPR} but their asymptotic behavior was still unclear. We use here a new numerical approximation of these traveling waves which shows that some traveling waves connect the two homogeneous steady states $0$ and $1$, which is a striking fact since $0$ is dynamically unstable and $1$ is unstable in the sense of Turing.

1: Laboratoire Jacques-Louis Lions (LJLL)
CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
2: BANG (INRIA Rocquencourt)
INRIA – Laboratoire Jacques-Louis Lions

hal-00537986, version 1
http://hal.archives-ouvertes.fr/hal-00537986
oai:hal.archives-ouvertes.fr:hal-00537986
From: Min Tang <>
Submitted on: Friday, 19 November 2010 19:53:58
Updated on: Thursday, 25 November 2010 11:33:40

See detailed view

Associated documents

PDF :

PS :

arXiv: 1011.4561

Export

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Documents without publication reference (Preprint)</head>
<biblStruct type="article" xml:id="hal-00537986"><analytic>
<author><persName><forename>Gregoire</forename><surname>Nadin</surname></persName>
<affiliation>
<orgName type="laboratory">LJLL</orgName>
<orgName type="team">Laboratoire Jacques-Louis Lions</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7598</orgName>
<orgName type="institution">Université Pierre et Marie Curie [UPMC] - Paris VI</orgName>
</affiliation>
</author>
<author><persName><forename>Benoit</forename><surname>Perthame</surname></persName>
<affiliation>
<orgName type="laboratory">LJLL</orgName>
<orgName type="team">Laboratoire Jacques-Louis Lions</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7598</orgName>
<orgName type="institution">Université Pierre et Marie Curie [UPMC] - Paris VI</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">INRIA Rocquencourt</orgName>
<orgName type="team">BANG</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">Laboratoire Jacques-Louis Lions</orgName>
</affiliation>
</author>
<author><persName><forename>Min</forename><surname>Tang</surname></persName>
<affiliation>
<orgName type="laboratory">INRIA Rocquencourt</orgName>
<orgName type="team">BANG</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">Laboratoire Jacques-Louis Lions</orgName>
</affiliation>
</author>
<title type="main" level="a">Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation</title></analytic><monogr><imprint/></monogr><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00537986</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00537986/PDF/report.pdf</idno></biblStruct>
</listBibl>
</listBibl>