Some effects of nonlocal diffusion on the solutions of Fisher-KPP equations in disconnected domains
type: Item
instance of: scholarly article
title: Some effects of nonlocal diffusion on the solutions of Fisher-KPP equations in disconnected domains
author: Alexis Léculier
author: J. M. Roquejoffre
published in: Calculus of Variations and Partial Differential Equations
publication date: 2022-11-18T00:00:00Z
review text: The paper studies an elliptic Fisher-KPP equation, with diffusion driven by the fractional Laplacian. The equation is set on a fragmented domain, i.e., the -- possibly, infinite -- union of components, resulting in a possibly unbounded domain. Under spectral and geometrical assumptions on such domain, the authors prove existence and uniqueness of solutions to the equation when coupled with homogeneous external Dirichlet conditions. It has to be stressed how existence and uniqueness are peculiar consequences of the nonlocality of the leading operator, allowing for connected components to exchange information with each other. The analysis is complemented by a double-sided estimate on the solutions and the inspection of the behaviour (especially continuity) of the principal eigenvalue in the particular case of dimension one and of a domain made up of two patches.
reviewed by: Nicola Abatangelo
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J61
zbMATH DE Number: 7620716
zbMATH Keywords: non-trivial bounded steady states
zbMATH Keywords: fragmented domain
zbMATH Keywords: exterior Dirichlet conditions
Wikidata QID: Q115385786
MaRDI profile type: Publication
full work available at URL: s00526-022-02374-6
OpenAlex ID: W4308748250
cites work: Q4746129
cites work: Le nombre de solutions de certains problèmes semi-linéaires elliptiques
cites work: Analysis of the periodically fragmented environment model. I: Species persistence
cites work: An Extension Problem Related to the Fractional Laplacian
cites work: An introduction to Sobolev spaces and interpolation spaces
cites work: Hitchhiker's guide to the fractional Sobolev spaces
cites work: Persistence criteria for populations with non-local dispersion
cites work: Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains
cites work: The role of the range of dispersal in a nonlocal Fisher-KPP equation: An asymptotic analysis
cites work: On simple eigenvalues of the fractional Laplacian under removal of small fractional capacity sets
cites work: Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Dirichlet region
cites work: Propagation in a fractional reaction-diffusion equation in a periodically hostile environment
cites work: The boundary Harnack principle for the fractional Laplacian
cites work: The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
cites work: Hopf's lemma and constrained radial symmetry for the fractional Laplacian
cites work: Holder estimates for solutions of integro differential equations like the fractional laplace
cites work: Regularity theory for fully nonlinear integro-differential equations
cites work: Removable singularities of solutions of elliptic equations
cites work: Q4693180
DOI: 10.1007/S00526-022-02374-6
description: scientific article; zbMATH DE number 7620716