A LOGISTIC EQUATION WITH NONLOCAL INTERACTIONS

作者：Caffarelli, Luis^*; Dipierro, Serena; Valdinoci, Enrico

来源：Kinetic and Related Models, 2017, 10(1): 141-170.

DOI：10.3934/krm.2017006

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

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 Levy 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.

• 出版日期2017-3