Hyperbolic extensions of constrained PDEs

Autor:	Abalos, Fernando, Reula, Oscar, Hilditch, David
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs General Relativity and Quantum Cosmology
Druh dokumentu:	Working Paper
Popis:	Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of the well-posedness of the Cauchy problem for these systems. Presently we review the use of hyperbolic reductions, in which the evolution equations are singled out for consideration. We then examine in greater detail the extensions, in which constraints are evolved as auxiliary variables alongside the original variables. Assuming a particular structure of the original system, we give sufficient conditions for strong-hyperbolicity of an extension. This theory is then applied to the examples of electromagnetism and a toy for magnetohydrodynamics. Comment: Contribution submitted to Frontiers in Physics special issue "Quasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary Approach"
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.18286 Zobrazit plný text záznamu View this record from Arxiv