Approximations of Random Dispersal Operators/Equations by Nonlocal Dispersal Operators/Equations

Abstract

This paper is concerned with the approximations of random dispersal operators/equations by nonlocal dispersal operators/equations. It first proves that the solutions of properly rescaled nonlocal dispersal initial-boundary value problems converge to the solutions of the corresponding random dispersal initial-boundary value problems. Next, it proves that the principal spectrum points of nonlocal dispersal operators with properly rescaled kernels converge to the principal eigenvalues of the corresponding random dispersal operators. Finally, it proves that the unique positive time periodic solutions of nonlocal dispersal KPP equations with properly rescaled kernels converge to the unique positive time periodic solutions of the corresponding random dispersal KPP equations.

28 pages

References in corpus (4)

• On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators
• Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity
• Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations
• Spreading Speeds and Traveling Waves of Nonlocal Monostable Equations in Time and Space Periodic Habitats