Non-Local Anisotropic Dispersal with Monostable Nonlinearity
Jerome Coville, Juan Davila,and Salome Martinez
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Submission date: 25. Jun. 2007
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
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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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.