A study of nonlocal spatially heterogeneous logistic equation with\n harvesting

2020/11/09 by Anup Biswas, Mitesh Modasiya, Biswas, Anup +1
Mathematics · #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.2011.04431

Abstract

We study a class of nonlocal reaction-diffusion equations with a harvesting\nterm where the nonlocal operator is given by a Bernstein function of the\nLaplacian. In particular, it includes the fractional Laplacian, fractional\nrelativistic operators, sum of fractional Laplacians of different order etc. We\nstudy existence, uniqueness and multiplicity results of the solutions to the\nsteady state equation. We also consider the parabolic counterpart and establish\nthe long time asymptotic of the solutions. Our proof techniques rely on both\nanalytic and probabilistic arguments.\n

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