Properties of positive solution for nonlocal reaction-diffusion equation with nonlocal boundary

Abstract

This paper considers the properties of positive solutions for a nonlocal equation with nonlocal boundary condition u (x, t) = ∫Ω f(x, y) u(y, t)dy on ∂Ω × (0,T). The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we establish the uniform blow-up estimates for the blow-up solution.