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MiS Preprint
30/2007
A nonlocal inhomogeneous dispersal process
Carmen Cortazar, Jerome Coville, Manuel Elgueta and Salome Martinez
Abstract
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.
