Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources

Abstract

This paper investigates the local existence of the nonnegative solution and the finite time blow-up of solutions and boundary layer profiles of diffusion equations with nonlocal reaction sources; we also study the global existence and that the rate of blow-up is uniform in all compact subsets of the domain, the blow-up rate of ${\left|u\left(t\right)\right|}_{\infty }$ is precisely determined.