Hyperbolic extensions of constrained PDEs
Fil: Abalos, Fernando. Universitat de les Illes Balears. Departament de Física; España.
| Main Authors: | , , |
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| Other Authors: | |
| Format: | info:eu-repo/semantics/submittedVersion |
| Language: | eng |
| Published: |
2024
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| Subjects: | |
| Online Access: | http://hdl.handle.net/11086/554097 https://arxiv.org/abs/2410.18286 https://doi.org/10.48550/arXiv.2410.18286 |
| _version_ | 1825132241944051712 |
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| author | Abalos, Fernando Reula, Oscar Hilditch, David |
| author2 | https://orcid.org/0000-0001-7863-3711 |
| author_facet | https://orcid.org/0000-0001-7863-3711 Abalos, Fernando Reula, Oscar Hilditch, David |
| author_sort | Abalos, Fernando |
| collection | Repositorio Digital Universitario |
| description | Fil: Abalos, Fernando. Universitat de les Illes Balears. Departament de Física; España. |
| format | info:eu-repo/semantics/submittedVersion |
| id | rdu-unc.554097 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2024 |
| record_format | dspace |
| spelling | rdu-unc.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/ |
| spellingShingle | Analysis of PDEs (math.AP) General Relativity Quantum Cosmology (gr-qc) Abalos, Fernando Reula, Oscar Hilditch, David Hyperbolic extensions of constrained PDEs |
| title | 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_short | Hyperbolic extensions of constrained PDEs |
| title_sort | hyperbolic extensions of constrained pdes |
| topic | Analysis of PDEs (math.AP) General Relativity Quantum Cosmology (gr-qc) |
| url | http://hdl.handle.net/11086/554097 https://arxiv.org/abs/2410.18286 https://doi.org/10.48550/arXiv.2410.18286 |
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