Bistable travelling waves for nonlocal reaction diffusion equations | Zendy

Matthieu Alfaro | Zendy; Jérôme Coville | Zendy; Gaël Raoul | Zendy

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Bistable travelling waves for nonlocal reaction diffusion equations

Author(s) -

Matthieu Alfaro,

Jérôme Coville,

Gaël Raoul

Publication year - 2013

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2014.34.1775

Subject(s) - bistability , traveling wave , reaction–diffusion system , physics , diffusion , nonlinear system , stability (learning theory) , classical mechanics , steady state (chemistry) , mathematical analysis , mathematics , thermodynamics , quantum mechanics , computer science , chemistry , machine learning

We are concerned with travelling wave solutions arising in a reac- tion di_usion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium u _ 1 is not assumed. We construct a travelling wave solution connecting 0 to an unknown steady state, which is \above and away" from the intermediate equilibrium. For focusing kernels we prove that, as expected, the wave connects 0 to 1. Our results also apply readily to the nonlocal ignition cas

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