Non-Local Anisotropic Dispersal with Monostable Nonlinearity

Jerome Coville, Juan Davila, and Salome Martinez

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Submission date: 25. Jun. 2007
Pages: 34
published in: Journal of differential equations, 244 (2008) 12, p. 3080-3118 
DOI number (of the published article): 10.1016/j.jde.2007.11.002
Bibtex
MSC-Numbers: 45K05, 47G20, 45J05
Keywords and phrases: Anisotropic nonlocal reaction diffusion equation, existence and uniqueness of travelling waves, asymptotic behavior's, Maximum principle and sliding technics
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Abstract:
We study the travelling wave problem

with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for . For c=0 we show examples of non-uniqueness.