Finite Difference Method for Nonlinear Time Degenerate Paraboltc Equations

Abstract

The aim of the paper is to extend the well known method of upper -lower solutions for continuous parabolic problem to finite difference system of nonlinear time degenerate parabolic Dirichlet initial boundary value problem. The central idea of this method is to develop iterative scheme based on the notion of upper and lower solutions. Using upper and lower solutions as distinct initial iterations, two monotone sequences are constructed. Existence-Comparison and uniqueness results for the solution of the nonlinear finite difference system are also developed. Positivity lemma is the main ingradient used in the proof of these results.