A logistic equation with nonlocal interactions

By Luis Caffarelli, Serena Dipierro, Enrico Valdinoci. 2016

49 citations recorded by the source corpus.

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:   $ \bullet $bounded domains,   $ \bullet $periodic environments,   $ \bullet $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.

Subfields: Applied Mathematics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/10aa648a257495183900ca1c1696a93a6f783852

Citations in the corpus

• Linear theory for a mixed operator with Neumann conditions (2020, unknown): “…followed by several species, as confirmed by a number of experimental data, see e.g. [56], and theoretically studied under several perspectives, see e.g. [3,5,11,15,20,22–24, As usual, the mathematical framework in (1) is endowed by a spatial domain on which the corresponding equation takes place.”