A logistic equation with nonlocal interactions

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Abstract

We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a Lévy process and can reach resources in a neighborhood of their position, we compare (and find explicit threshold for survival) the local and nonlocal case. As ambient space, we can consider: • bounded domains, • periodic environments, • transition problems, where the environment consists of a block of infinitesimal diffusion and an adjacent nonlocal one. In each of these cases, we analyze the existence/nonexistence of solutions in terms of the spectral properties of the domain. In particular, we give a detailed description of the fact that nonlocal populations may better adapt to sparse resources and small environments.

Original languageEnglish
Pages (from-to)141-170
Number of pages30
JournalKinetic and Related Models
Volume10
Issue number1
DOIs
Publication statusPublished - 2017

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