WIAS Preprint No. 2216, (2016)

A logistic equation with nonlocal interactions



Authors

  • Caffarelli, Luis
  • Dipierro, Serena
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35Q92 46N60 35R11 60G22

Keywords

  • Mathematical models for biology, local and nonlocal dispersals, spectral analysis, existence of nontrivial solutions

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: beginitemize item bounded domains, item periodic environments, item transition problems, where the environment consists of a block of infinitesimal diffusion and an adjacent nonlocal one. enditemize 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.

Appeared in

  • Kinet. Relat. Models, 10:1 (2017) pp. 141--170.

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