MONOTONE TECHNIQUE FOR NONLINEAR DEGENERATE WEAKLY COUPLED SYSTEM OF PARABOLIC PROBLEMS

The purpose of this paper is to develop monotone technique by introducing the notion of upper and lower solutions together with the associated monotone iterations for nonlinear weakly coupled time degenerate parabolic system with initial and boundary conditions. Under suitable initial iterations and for mixed quasimonotone boundary functions, two monotone sequences are constructed. It is shown that these two sequences converge monotonically from above and below respectively to maximal and minimal solutions of Dirichlet initial boundary value problem for nonlinear weakly coupled time degenerate parabolic system which leads to existence-comparison and uniqueness results for the solution of the Dirichlet initial boundary value problem for nonlinear weakly coupled time degenerate parabolic system.