Examples of PDEs all whose points are characteristic

Rosado María, María Eugenia (2011). Examples of PDEs all whose points are characteristic. In: "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.

Description

Title: Examples of PDEs all whose points are characteristic
Author/s:
  • Rosado María, María Eugenia
Item Type: Presentation at Congress or Conference (Article)
Event Title: ESF exploratory workshop onCurrent Problems in Differential Calculus over Commutative Algebras,Secondary Calculus, and Solution Singularities of Non-Linear PDEs
Event Dates: 13/06/2011 - 16/06/2011
Event Location: Vietri sul Mare, Salerno, Italia
Title of Book: Proceedings of ESF exploratory workshop onCurrent Problems in Differential Calculus over Commutative Algebras,Secondary Calculus, and Solution Singularities of Non-Linear PDEs
Date: 2011
Subjects:
Faculty: E.T.S. Arquitectura (UPM)
Department: Matemática Aplicada a la Edificación, al Medio Ambiente y al Urbanismo [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

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]

More information

Item ID: 11589
DC Identifier: http://oa.upm.es/11589/
OAI Identifier: oai:oa.upm.es:11589
Deposited by: Memoria Investigacion
Deposited on: 18 Jul 2012 08:08
Last Modified: 31 Mar 2020 09:40
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