Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations

Handle URI:
http://hdl.handle.net/10754/621511
Title:
Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
Authors:
Figalli, Alessio; Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Marcon, Diego
Abstract:
Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Figalli A, Gomes D, Marcon D (2016) Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations. Calculus of Variations and Partial Differential Equations 55. Available: http://dx.doi.org/10.1007/s00526-016-1016-5.
Publisher:
Springer Nature
Journal:
Calculus of Variations and Partial Differential Equations
Issue Date:
23-Jun-2016
DOI:
10.1007/s00526-016-1016-5
Type:
Article
ISSN:
0944-2669; 1432-0835
Sponsors:
A. Figalli is partially supported by the NSF Grants DMS-1262411 and DMS-1361122. D. Gomes was partially supported by KAUST baseline and start-up funds. D. Marcon was partially supported by the UT Austin-Portugal partnership through the FCT doctoral fellowship SFRH/BD/33919/2009.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFigalli, Alessioen
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorMarcon, Diegoen
dc.date.accessioned2016-11-03T08:31:05Z-
dc.date.available2016-11-03T08:31:05Z-
dc.date.issued2016-06-23en
dc.identifier.citationFigalli A, Gomes D, Marcon D (2016) Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations. Calculus of Variations and Partial Differential Equations 55. Available: http://dx.doi.org/10.1007/s00526-016-1016-5.en
dc.identifier.issn0944-2669en
dc.identifier.issn1432-0835en
dc.identifier.doi10.1007/s00526-016-1016-5en
dc.identifier.urihttp://hdl.handle.net/10754/621511-
dc.description.abstractHere, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipA. Figalli is partially supported by the NSF Grants DMS-1262411 and DMS-1361122. D. Gomes was partially supported by KAUST baseline and start-up funds. D. Marcon was partially supported by the UT Austin-Portugal partnership through the FCT doctoral fellowship SFRH/BD/33919/2009.en
dc.publisherSpringer Natureen
dc.subject35F21en
dc.titleWeak KAM theory for a weakly coupled system of Hamilton–Jacobi equationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalCalculus of Variations and Partial Differential Equationsen
dc.contributor.institutionDepartment of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX, United Statesen
dc.contributor.institutionInstituto de Matemática e Estatístíca, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazilen
kaust.authorGomes, Diogo A.en
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