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MiS Preprint

A nonlocal inhomogeneous dispersal process

Carmen Cortazar, Jerome Coville, Manuel Elgueta and Salome Martinez


This article in devoted to the the study of the nonlocal dispersal equation $$u_t (x,t)= \int_{\mathbb{R}} J\left(\frac{x-y}{g(y)}\right)\frac{u(y,t)}{g(y)} dy - u(x,t) \ \mbox{ in } \mathbb{R} \times [0,\infty ),$$ and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on $g$ and $J$, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as $t\to \infty$, showing that they converge locally to zero.

Mar 23, 2007
May 26, 2008
MSC Codes:
47G20, 45K05, 35K90, 35M99
integral equation, non local dispersal, inhomogeneous dispersal

Related publications

2007 Repository Open Access
C. Cortázar, Jérôme Coville, M. Elgueta and Salomé Martinez

A nonlocal inhomogeneous dispersal process

In: Journal of differential equations, 241 (2007) 2, pp. 332-358