A study of nonlocal spatially heterogeneous logistic equation with harvesting. (January 2022)

• Record Type: Journal Article
• Authors: Biswas, Anup; Modasiya, Mitesh
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: primary 35R11 35S15 35K57 -- secondary 35J60 92D25; Bernstein functions of the Laplacian -- Nonlocal semipositone problems -- Long time behaviour -- Nonlocal Fisher–KPP -- Bifurcation -- Variable order nonlocal kernel; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112599
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study a class of nonlocal reaction–diffusion equations with a harvesting term where the nonlocal operator is given by a Bernstein function of the Laplacian. In particular, it includes the fractional Laplacian, fractional relativistic operators, sum of fractional Laplacians of different order etc. We study the existence, uniqueness and multiplicity results of the solutions to the steady state equation. We also consider the parabolic counterpart and establish the long time asymptotic of the solutions. Our proof techniques rely on both analytic and probabilistic arguments.