On Global Existence of Solutions of Initial Boundary Value Problem for a System of Semilinear Parabolic Equations with Nonlinear Nonlocal Neumann Boundary Conditions

Abstract

We establish conditions for the existence and nonexistence of global solutions of initial boundary value problem for a system of semilinear parabolic equations with nonlinear nonlocal Neumann boundary conditions. We show that these conditions are determined by the behavior of the problem coefficients as t→∞.