Monotone Iterative Method for a System of Nonlocal Initial-Boundary Parabolic Problems

The aim of the paper is to prove a theorem about the existence and uniqueness of a classical solution of a system of nonlinear nonlocal initial-boundary parabolic problems. For this purpose a monotone iterative method and a theorem about the weak parabolic functional-differential inequalities are used. The paper is a continuation of the papers of Byszewski (J. Appl. Math. Stochastic Anal.5 (1992), 43-68) and Byszewski and Lakshmikantham (J. Math. Phys. Sci., to appear), and generalizes some results from Brzychczy (Ann. Polon. Math.42 (1983), 37-43) and Chabrowski (Funkcial. Ekvac.27 (1984), 101-123).