Stable Manifold Approximation for the Heat Equation with Nonlinear Boundary Condition

Abstract

In this paper we study the dynamic behavior of positive solutions of the heat equation in one space dimension with a nonlinear flux boundary condition of the type ux=up−u at x=1. We analyze the behavior of a semidiscrete numerical scheme in order to approximate the stable manifold of the only positive steady solution. We also obtain some stability properties of this positive steady solution and a description of its table manifold.