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Rosado María, María Eugenia ORCID: https://orcid.org/0000000229305612 (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 NonLinear PDEs", 13/06/2011  16/06/2011, Vietri sul Mare, Salerno, Italia.
Title:  Examples of PDEs all whose points are characteristic 

Author/s: 

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 NonLinear 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 NonLinear 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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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) 20132036]. The notion of a characteristic hypersurface for an arbitrary firstorder PDE system on an ar bitrary bred manifold π : P → M, is introduced and for the systems dened by the EulerLagrange equations of Lijk every hypersurface is shown to be characteristic. The EulerLagrange 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 CauchyKowaleska 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), 119155]
Item ID:  11589 

DC Identifier:  https://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 