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A nonlocal inhomogeneous dispersal process

Abstract : 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
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Submitted on : Saturday, May 30, 2020 - 11:15:58 PM
Last modification on : Sunday, September 20, 2020 - 3:58:01 PM

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C. Cortázar, Jerome Coville, M. Elgueta, S. Martinez. A nonlocal inhomogeneous dispersal process. Journal of Differential Equations, Elsevier, 2007, 241 (2), pp.332-358. ⟨10.1016/j.jde.2007.06.002⟩. ⟨hal-02661991⟩

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