Hyperbolic extensions of constrained PDEs

Fil: Abalos, Fernando. Universitat de les Illes Balears. Departament de Física; España.

Guardado en:
Detalles Bibliográficos
Autores principales: Abalos, Fernando, Reula, Oscar, Hilditch, David
Otros Autores: https://orcid.org/0000-0001-7863-3711
Formato: submittedVersion article
Lenguaje:Inglés
Publicado: 2024
Materias:
Analysis of PDEs (math.AP)
General Relativity
Quantum Cosmology (gr-qc)
Acceso en línea:http://hdl.handle.net/11086/554097
https://arxiv.org/abs/2410.18286
https://doi.org/10.48550/arXiv.2410.18286
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-554097
record_format dspace
spelling I10-R141-11086-5540972024-10-29T06:39:06Z Hyperbolic extensions of constrained PDEs Abalos, Fernando Reula, Oscar Hilditch, David https://orcid.org/0000-0001-7863-3711 https://orcid.org/0000-0003-2517-7454 https://orcid.org/0000-0001-9960-5293 Analysis of PDEs (math.AP) General Relativity Quantum Cosmology (gr-qc) info:eu-repo/semantics/submittedVersion Fil: Abalos, Fernando. Universitat de les Illes Balears. Departament de Física; España. Fil: Abalos, Fernando. Universitat de les Illes Balears. Institute of Applied Computing and Community Code; España. Fil: Reula, Oscar. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Reula, Oscar. Consejo Nacional de Investigaciones Científicas y Tecnológicas. instituto de Física Enrique Gaviola; Argentina. Fil: Hilditch, David. Universidade de Lisboa. Departamento de Física, Instituto Superior Técnico IST; Portugal. 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. info:eu-repo/semantics/submittedVersion Fil: Abalos, Fernando. Universitat de les Illes Balears. Departament de Física; España. Fil: Abalos, Fernando. Universitat de les Illes Balears. Institute of Applied Computing and Community Code; España. Fil: Reula, Oscar. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Reula, Oscar. Consejo Nacional de Investigaciones Científicas y Tecnológicas. instituto de Física Enrique Gaviola; Argentina. Fil: Hilditch, David. Universidade de Lisboa. Departamento de Física, Instituto Superior Técnico IST; Portugal. 2024-10-28T20:06:12Z 2024-10-28T20:06:12Z 2024-10-23 article Abalos, F., Reula, O., & Hilditch, D. (2024). Hyperbolic extensions of constrained PDEs. arXiv preprint arXiv:2410.18286. http://hdl.handle.net/11086/554097 https://arxiv.org/abs/2410.18286 https://doi.org/10.48550/arXiv.2410.18286 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Analysis of PDEs (math.AP)
General Relativity
Quantum Cosmology (gr-qc)
spellingShingle Analysis of PDEs (math.AP)
General Relativity
Quantum Cosmology (gr-qc)
Abalos, Fernando
Reula, Oscar
Hilditch, David
Hyperbolic extensions of constrained PDEs
topic_facet Analysis of PDEs (math.AP)
General Relativity
Quantum Cosmology (gr-qc)
description Fil: Abalos, Fernando. Universitat de les Illes Balears. Departament de Física; España.
author2 https://orcid.org/0000-0001-7863-3711
author_facet https://orcid.org/0000-0001-7863-3711
Abalos, Fernando
Reula, Oscar
Hilditch, David
format submittedVersion
article
author Abalos, Fernando
Reula, Oscar
Hilditch, David
author_sort Abalos, Fernando
title Hyperbolic extensions of constrained PDEs
title_short Hyperbolic extensions of constrained PDEs
title_full Hyperbolic extensions of constrained PDEs
title_fullStr Hyperbolic extensions of constrained PDEs
title_full_unstemmed Hyperbolic extensions of constrained PDEs
title_sort hyperbolic extensions of constrained pdes
publishDate 2024
url http://hdl.handle.net/11086/554097
https://arxiv.org/abs/2410.18286
https://doi.org/10.48550/arXiv.2410.18286
work_keys_str_mv AT abalosfernando hyperbolicextensionsofconstrainedpdes
AT reulaoscar hyperbolicextensionsofconstrainedpdes
AT hilditchdavid hyperbolicextensionsofconstrainedpdes
_version_ 1824552414332583936

Ejemplares similares