Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Multi-time systems of conservation laws

Authors: Aldo Bazan, Paola Loreti and Wladimir Neves
Journal: Quart. Appl. Math. 72 (2014), 491-511
MSC (2010): Primary 54C40, 14E20; Secondary 46E25, 20C20
DOI: https://doi.org/10.1090/S0033-569X-2014-01341-3
Published electronically: June 25, 2014
MathSciNet review: 3237561
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Abstract | References | Similar Articles | Additional Information

Abstract: Motivated by the work of P. L. Lions and J.-C. Rochet (1986) concerning multi-time Hamilton-Jacobi equations, we introduce the theory of multi-time systems of conservation laws. We show the existence and uniqueness of solution to the Cauchy problem for a system of multi-time conservation laws with two independent time variables in one space dimension. Our proof relies on a suitable generalization of the Lax-Oleinik formula.

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Additional Information

Aldo Bazan
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Cidade Universitária 21945-970, Rio de Janeiro, Brazil
Email: aabp2003@pg.im.ufrj.br

Paola Loreti
Affiliation: Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, via A. Scarpa n.16 00161 Roma
Email: paolaloreti@gmail.com

Wladimir Neves
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Cidade Universitária 21945-970, Rio de Janeiro, Brazil
Email: wladimir@im.ufrj.br

DOI: https://doi.org/10.1090/S0033-569X-2014-01341-3
Keywords: Conservation laws, Hamilton-Jacobi equations, Cauchy problem, multi-time partial differential equations.
Received by editor(s): June 29, 2012
Published electronically: June 25, 2014
Additional Notes: Aldo Bazan is supported by FAPERJ by the grant 2009.2848.0.
Wladimir Neves is partially supported by FAPERJ through the grant E-26/ 111.564/2008 entitled \sl“Analysis, Geometry and Applications” and by Pronex-FAPERJ through the grant E-26/ 110.560/2010 entitled \textsl{"Nonlinear Partial Differential Equations"}.
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