Uniform Boundedness and Global Existence of Solutions to a Quasilinear Diffusion Equation with Nonlocal Fisher-KPP Type Reaction Term

Abstract

This paper deals with the Cauchy problem and Neumann initial boundary value problem for a quasilinear diffusion equation with nonlocal Fisher-KPP type reaction terms. We establish the uniform boundedness and global existence of solutions to the problems by using multipliers technique and modified Moser's iteration argument for some ranges of parameters. Moreover, the ranges of parameters have similar structure to that of the classical critical Fujita exponent.