Hamilton-Jacobi equations on networks

Yves Achdou; Fabio Camilli; Alessandra Cutri; Nicoletta Tchou

hal-00503910, version 1

Hamilton-Jacobi equations on networks

Yves Achdou () ¹, Fabio Camilli () ², Alessandra Cutri ³, Nicoletta Tchou () ⁴

Résumé : We consider continuous-state and continuous-time control problem where the admissible trajectories of the system are constrained to remain on a network. Under suitable assumptions, we prove that the value function is continuous. We define a notion of viscosity solution of Hamilton-Jacobi equations on the network for which we prove a comparison principle. The value function is thus the unique viscosity solution of the Hamilton-Jacobi equation on the network.

1 : Laboratoire Jacques-Louis Lions (LJLL)
CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
2 : Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate (MeMoMat)
Universita di Roma "La Sapienza"
3 : Dipartimento di Matematica [Roma II] (DIPMAT)
Universita degli studi di Roma Tor Vergata
4 : Institut de Recherche Mathématique de Rennes (IRMAR)
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

hal-00503910, version 1
http://hal.archives-ouvertes.fr/hal-00503910
oai:hal.archives-ouvertes.fr:hal-00503910
Contributeur : Marie-Annick Guillemer <>
Soumis le : Lundi 19 Juillet 2010, 12:01:06
Dernière modification le : Lundi 19 Juillet 2010, 13:06:52

Voir la fiche détaillée

Documents associés

PDF :

Exporter

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Documents sans référence de publication (Preprint)</head>
<biblStruct type="article" xml:id="hal-00503910"><analytic>
<author><persName><forename>Yves</forename><surname>Achdou</surname></persName>
<affiliation>
<orgName type="laboratory">LJLL</orgName>
<orgName type="team">Laboratoire Jacques-Louis Lions</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7598</orgName>
<orgName type="institution">Université Pierre et Marie Curie [UPMC] - Paris VI</orgName>
</affiliation>
</author>
<author><persName><forename>Fabio</forename><surname>Camilli</surname></persName>
<affiliation>
<orgName type="laboratory">MeMoMat</orgName>
<orgName type="team">Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate</orgName>
<country>IT</country>
<orgName type="institution">Universita di Roma "La Sapienza"</orgName>
</affiliation>
</author>
<author><persName><forename>Alessandra</forename><surname>Cutri</surname></persName>
<affiliation>
<orgName type="laboratory">DIPMAT</orgName>
<orgName type="team">Dipartimento di Matematica [Roma II]</orgName>
<country>IT</country>
<orgName type="institution">Universita degli studi di Roma Tor Vergata</orgName>
</affiliation>
</author>
<author><persName><forename>Nicoletta</forename><surname>Tchou</surname></persName>
<affiliation>
<orgName type="laboratory">IRMAR</orgName>
<orgName type="team">Institut de Recherche Mathématique de Rennes</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR6625</orgName>
<orgName type="institution">Université de Rennes 1</orgName>
<orgName type="institution">École normale supérieure de Cachan - ENS Cachan</orgName>
<orgName type="institution">Institut National des Sciences Appliquées (INSA) : - RENNES</orgName>
<orgName type="institution">Université de Rennes II - Haute Bretagne</orgName>
</affiliation>
</author>
<title type="main" level="a">Hamilton-Jacobi equations on networks</title></analytic><monogr><imprint/></monogr><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00503910</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00503910/PDF/network_14luglio.pdf</idno></biblStruct>
</listBibl>
</listBibl>