Comptes Rendus
no. 17-18
Partial Differential Equations/Optimal Control
A Hamilton–Jacobi PDE in the space of measures and its associated compressible Euler equations
[Une EDP de Hamilton–Jacobi dans lʼespace des mesures et ses équations dʼEuler compressibles associées]

Présenté par : the Editorial Board

Jin Feng1
1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 973-976.

Nous introduisons une classe dʼintégrales dʼaction définies sur lʼespace des chemins à valeurs mesures de probabilité. Dans ce contexte lʼaction minimale existe et donne une solution faible dʼune équation dʼEuler compressible. Nous montrons que lʼéquation de Hamilton Jacobi associʼee à la formulation variationnelle de lʼéquation dʼEuler est bien posée dans le sens des solutions de viscosité.

We introduce a class of action integrals defined over probability-measure-valued path space. Minimal action exists in this context and gives weak solution to a compressible Euler equation. We prove that the Hamilton–Jacobi PDE associated with such variational formulation of Euler equation is well posed in viscosity solution sense.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.08.013
Jin Feng 1

1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA 
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Jin Feng. A Hamilton–Jacobi PDE in the space of measures and its associated compressible Euler equations. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 973-976. doi : 10.1016/j.crma.2011.08.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.013/

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[3] J. Feng; T. Kurtz Large Deviation for Stochastic Processes, Mathematical Surveys and Monographs, vol. 131, American Mathematical Society, Providence, RI, 2006

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