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MiS Preprint
58/2007
Non-Local Anisotropic Dispersal with Monostable Nonlinearity
Jerome Coville, Juan Davila and Salome Martinez
Abstract
We study the travelling wave problem $$ J\star u -u -cu^{\prime}+f(u)=0\quad{ in } \quad \mathbb{R}, \quad u(-\infty)=0, \quad u(+\infty)=1 $$ 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 $c\not=0$. For $c=0$ we show examples of non-uniqueness.
Anisotropic nonlocal reaction diffusion equation, existence and uniqueness of travelling waves, asymptotic behavior's, Maximum principle and sliding technics
Related publications
inJournal
2008
Repository Open Access
Jérôme Coville, Juan Dávila and Salomé Martinez
Nonlocal anisotropic dispersal with monostable nonlinearity
In: Journal of differential equations, 244 (2008) 12, pp. 3080-3118
