Blowing-up and asymptotic behaviour of solutions for a finite difference system

Abstract

This paper is concerned with the dynamics of a system of nonlinear finite difference equations which arise from a class of parabolic boundary-value problems. The main purpose is the determination of a critical physical parameter σ^* such that for σ<σ^* a unique global solution u_n, to the algebraic system exists and converges to a “steady-state” solution as n→∞ while for σ>^* the solution blows up at some finite n^*. Also discussed is the convergence and blowing up property of u_n, for various initial vector u_o whenσ< σ^*.

Keywords:

• finite difference equations
• asymptotic behaviour
• blowing-up of solution
• method of upper and lower solutions