Quasi-linear symmetric hyperbolic Fuchsian systems in several space dimensions

TL;DR

This paper proves existence and uniqueness for a class of quasilinear symmetric hyperbolic Fuchsian PDEs in multiple spatial dimensions, extending previous one-dimensional results.

Contribution

It extends earlier one-dimensional results to multiple space dimensions for quasilinear symmetric hyperbolic Fuchsian systems.

Findings

Existence of solutions in several space dimensions.

Uniqueness of solutions for the class of PDEs.

Generalization of previous one-dimensional results.

Abstract

We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an extension of earlier work by the authors for the same problem in one space dimension.