Perron's method for quasilinear hyperbolic systems: Part I

Abstract

We define a notion of viscosity solution (sub-, supersolution) for these systems, prove a comparison principle and we prove existence of viscosity solutions using a Perron like method. In Part I, we do all the above except prove existence using the Perron method.  2005 Elsevier Inc. All rights reserved.

Perron's method for quasilinear hyperbolic systems, Part II

“…Also note that the Banach spaces we used have the property that when t = ∞, they are contained in the Banach spaces of the same type when t is a finite T . Thus the comparison theorems of Section 5 of Part I [6] and the Difference Criterion of Section 6 of Part I [6] still hold. Then, we see that all our results still hold.…”