Stable Manifold Approximation For The Heat Equation With Nonlinear Boudary Condition

ACOSTA, GABRIEL; JULIAN FERNANDEZ BONDER; ROSSI, JULIO DANIEL

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS

SPRINGER

Año: 2000 vol. 12 p. 557 - 578

1040-7294

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 numeri- cal 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.