Examples of PDEs all whose points are characteristic

Rosado Maria, Maria Eugenia (2011). Examples of PDEs all whose points are characteristic. En: "ESF exploratory workshop onCurrent Problems in Differential Calculus over Commutative Algebras,Secondary Calculus, and Solution Singularities of Non-Linear PDEs", 13/06/2011 - 16/06/2011, Vietri sul Mare, Salerno, Italia.

Descripción

Título: Examples of PDEs all whose points are characteristic
Autor/es:
  • Rosado Maria, Maria Eugenia
Tipo de Documento: Ponencia en Congreso o Jornada (Sin especificar)
Título del Evento: ESF exploratory workshop onCurrent Problems in Differential Calculus over Commutative Algebras,Secondary Calculus, and Solution Singularities of Non-Linear PDEs
Fechas del Evento: 13/06/2011 - 16/06/2011
Lugar del Evento: Vietri sul Mare, Salerno, Italia
Título del Libro: Proceedings of ESF exploratory workshop onCurrent Problems in Differential Calculus over Commutative Algebras,Secondary Calculus, and Solution Singularities of Non-Linear PDEs
Fecha: 2011
Materias:
Escuela: E.T.S. Arquitectura (UPM)
Departamento: Matemática Aplicada a la Edificación, al Medio Ambiente y al Urbanismo [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

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ID de Registro: 11589
Identificador DC: http://oa.upm.es/11589/
Identificador OAI: oai:oa.upm.es:11589
Depositado por: Memoria Investigacion
Depositado el: 18 Jul 2012 08:08
Ultima Modificación: 20 Abr 2016 19:36
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