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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

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

Related publications

inJournal
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