Properties of solutions for a reaction–diffusion equation with nonlinear absorption and nonlinear nonlocal Neumann boundary condition

Abstract

In this paper, the authors consider the reaction-diffusion equation with nonlinear absorption and nonlinear nonlocal Neumann boundary condition. They prove that the solution either exists globally or blows up in finite time depending on the initial data, the weighting function on the border, and nonlinear indexes in the equation by using the comparison principle.