Traveling waves and long-time behavior in a doubly nonlocal Fisher-KPP equation

Abstract

We consider a Fisher-KPP-type equation, where both diffusion and nonlinear part are nonlocal, with anisotropic probability kernels. Under minimal conditions on the coefficients, we prove existence, uniqueness, and uniform space-time boundedness of the positive solution. We investigate existence, uniqueness, and asymptotic behavior of monotone traveling waves for the equation. We also describe the existence and main properties of the front of propagation.

100 pages, 3 figures

References in corpus (4)

• A microscopic probabilistic description of a locally regulated population and macroscopic approximations
• Nonlocal anisotropic dispersal with monostable nonlinearity
• Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity
• Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous media

Cited by in corpus (4)

• The hair-trigger effect for a class of nonlocal nonlinear equations
• Global stability in a nonlocal reaction-diffusion equation
• Doubly nonlocal Fisher-KPP equation: Existence and properties of traveling waves
• Persistence and time periodic positive solutions of doubly nonlocal Fisher-KPP equations in time periodic and space heterogeneous media