A study of nonlocal spatially heterogeneous logistic equation with harvesting. (January 2022) - Biswas, Anup; Modasiya, Mitesh
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.