A logistic equation with nonlocal interactions

Research output: Contribution to journalArticle

7 Citations (Scopus)

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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Nonlocal Interactions
Logistic Equation
Logistics
Resources
Process Modeling
Proliferation
Spectral Properties
Nonexistence
Bounded Domain
Adjacent
Term

Cite this

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title = "A logistic equation with nonlocal interactions",
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 L{\'e}vy 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.",
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A logistic equation with nonlocal interactions. / Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico.

In: Kinetic and Related Models, Vol. 10, No. 1, 2017, p. 141-170.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A logistic equation with nonlocal interactions

AU - Caffarelli, Luis

AU - Dipierro, Serena

AU - Valdinoci, Enrico

PY - 2017

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AB - 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.

KW - Existence of nontrivial solutions

KW - Local and nonlocal dispersals

KW - Mathematical models for biology

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