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MiS Preprint

Non-Local Anisotropic Dispersal with Monostable Nonlinearity

Jerome Coville, Juan Davila and Salome Martinez


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.

MSC Codes:
45K05, 47G20, 45J05
Anisotropic nonlocal reaction diffusion equation, existence and uniqueness of travelling waves, asymptotic behavior's, Maximum principle and sliding technics

Related publications

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