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dc.contributor.author
Abalos, Julio Fernando
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dc.date.available
2022-05-31T14:31:35Z
dc.date.issued
2018-11
dc.identifier.citation
Abalos, Julio Fernando; A necessary condition ensuring the strong hyperbolicity of first-order systems; World Scientific; Journal Of Hyperbolic Differential Equations; 16; 1; 11-2018; 193-221
dc.identifier.issn
0219-8916
dc.identifier.uri
http://hdl.handle.net/11336/158589
dc.description.abstract
We study strong hyperbolicity of first order partial differential equationsfor systems with differential constraints. In these cases, the number ofequations is larger than the unknown fields, therefore, the standard Kreissnecessary and sufficient conditions of strong hyperbolicity do not directlyapply. To deal with this problem one introduces a new tensor, called areduction, which selects a subset of equations with the aim of using them asevolution equations for the unknown. If that tensor leads to a stronglyhyperbolic system we call it a hyperbolizer. There might exist many of themor none.A question arises on whether a given system admits any hyperbolization atall. To sort-out this issue, we look for a condition on the system, suchthat, if it is satisfied, there is no hyperbolic reduction. To that purposewe look at the singular value decomposition of the whole system and studycertain one parameter families ($arepsilon $) of perturbations of theprincipal symbol. We look for the perturbed singular values around thevanishing ones and show that if they behave as $Oleft( arepsilon^{l}ight) $, with $lgeq 2$, then there does not exist any hyperbolizer.In addition, we further notice that the validity or failure of thiscondition can be established in a simple and invariant way.Finally we apply the theory to examples in physics, such as Force-FreeElectrodynamics in Euler potentials form and charged fluids with finiteconductivity. We find that they do not admit any hyperbolization.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
World Scientific
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Strong hyperbolicity
dc.subject
Evolution and constraint equations
dc.subject
Singular Value Decomposition
dc.subject
Force-Free Electrodynamic
dc.subject.classification
Física de Partículas y Campos
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dc.subject.classification
Ciencias Físicas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
A necessary condition ensuring the strong hyperbolicity of first-order systems
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-04-26T17:37:30Z
dc.identifier.eissn
1793-6993
dc.journal.volume
16
dc.journal.number
1
dc.journal.pagination
193-221
dc.journal.pais
Singapur
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dc.description.fil
Fil: Abalos, Julio Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
dc.journal.title
Journal Of Hyperbolic Differential Equations
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1142/S0219891619500073
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0219891619500073
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