A logistic equation with nonlocal interactions
- Caffarelli, Luis
- Dipierro, Serena
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35Q92 46N60 35R11 60G22
- 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 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.
- Kinet. Relat. Models, 10:1 (2017) pp. 141--170.