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

被引：49

作者：

Nadin, Gregoire ^{[1
]}

Perthame, Benoit ^{[1
,2
]}

Tang, Min ^{[1
,2
]}

机构：

[1] UPMC, CNRS, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[2] INRIA Paris Rocquencourt, Equipe BANG, F-78153 Le Chesnay, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2011年 / 349卷 / 9-10期

关键词：

D O I：

10.1016/j.crma.2011.03.008

中图分类号：

O1 [数学];

学科分类号：

070101 [基础数学];

摘要：

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 Berestycki et al. (2009) [3] 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. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：553 / 557

页数：5

共 7 条

[1]

[Anonymous], 1937, Bull. Univ. Mosc. Ser. Int. A, DOI DOI 10.1016/B978-0-08-092523-3.50014-9

[2]

SPATIAL STRUCTURES AND GENERALIZED TRAVELLING WAVES FOR AN INTEGRO-DIFFERENTIAL EQUATION [J].

Apreutesei, Narcisa ;

Bessonov, Nikolai ;

Volpert, Vitaly ;

Vougalter, Vitali .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2010, 13 (03) :537-557

[3]

Front propagation in periodic excitable media [J].

Berestycki, H ;

Hamel, F .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2002, 55 (08) :949-1032

[4]

The non-local Fisher-KPP equation: travelling waves and steady states [J].

Berestycki, Henri ;

Nadin, Gregoire ;

Perthame, Benoit ;

Ryzhik, Lenya .

NONLINEARITY, 2009, 22 (12) :2813-2844

[5]

Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources [J].

Genieys, S. ;

Volpert, V. ;

Auger, P. .

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2006, 1 (01) :63-80

[6]

Travelling front solutions of a nonlocal Fisher equation [J].

Gourley, SA .

JOURNAL OF MATHEMATICAL BIOLOGY, 2000, 41 (03) :272-284

[7]

TRAVELING PERIODIC-WAVES IN HETEROGENEOUS ENVIRONMENTS [J].

SHIGESADA, N ;

KAWASAKI, K ;

TERAMOTO, E .

THEORETICAL POPULATION BIOLOGY, 1986, 30 (01) :143-160

← 1 →