A nonlocal inhomogeneous dispersal process
Résumé
This article in devoted to the study of the nonlocal dispersal equation ut(x,t)=∫RJ(x−yg/y) u(y,t)/g(y) dy − u(x,t)in R×[0,∞), 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→∞, showing that they converge locally to zero