Quasi-linear symmetric hyperbolic Fuchsian systems in several space dimensions

2012/05/10 by Ellery Ames, Ames, Ellery, Florian Beyer +5
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.AP

paper · pdf · doi:10.48550/arxiv.1205.2166

21 pages

arxiv created 2012/09/05 · arxiv updated 2012/09/06

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.

Related

• Second-order hyperbolic Fuchsian systems. General theory
• On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations
• Global existence for semi-linear hyperbolic equations in a neighbourhood of future null infinity
• Solutions of first-order quasilinear systems expressed in Riemann invariants
• Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems