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Extended Monotone Methods for Hyperbolic Problems in Three Variables

We consider Initial-Boundary value problems associated with nonlinear hyperbolic partial dierential equation in three independent variables, in a general setting wherein the forcing function is a sum of two monotonic functions. Employing natural lower-upper and coupled lower-upper solutions, we develop iterative schemes which converge uniformly and monotonically to the minimal-maximal and cou- pled minimal-maximal solutions of the problem.