Iterative methods for quasilinear hyperbolic systems in the first canonic form

Abstract

Quasilinger hyberbolic equation and system in the “first canonic” (diagonal) from areconsidered, with both Cauchy data and boundary data “a la Cesari”, and an arbitrary number of independent variables. The aim of the paper is to develop iterative methods converging uniformly to the a.e. solution of the Cauchy or boundary value problem, based on a modified version of the proof of Cesari's original existence and uniqueness theorem and on some general results concerning contractive Lipschitz maps in the product of two Banach spaces, as derived in earlier papers. The existence proof given here is in fact founded on a new contraction map in the product of two (closed convex subsets of) Banach function spaces.

^†Research supported by the GNFM of CNR

^†Research supported by the GNFM of CNR

Notes

^†Research supported by the GNFM of CNR