THE DOMAIN DECOMPOSITION METHOD FOR MULTIDIMENSIONAL AND LARGE SCALE NONLINEAR SYSTEMS—CASE OF SUBDOMAINS OVERLAPPING

Abstract

In this article, we present the method of space domain decomposition for the initial-boundary value problem of a class of multidimensional nonlinear parabolic systems. Firstly, by discretization of the time t, we reduce the original problem to the boundary value problem of the nonlinear elliptic systems. Secondly, making use of the Leary-Schauder fixed point theorem, we prove the existence of the solution for this boundary value problem of elliptic type. Finally, applying the prior estimations, we prove the convergence of the semi-discrete solution.