Extended Monotone Methods for Hyperbolic Problems in Three Variables

摘要

We consider Initial-Boundary value problems associated with nonlinear hyperbolic partial differential 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 coupled minimal-maximal solutions of the problem.