Density large deviations for multidimensional stochastic hyperbolic conservation laws

Abstract : We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the conductivity and dif-fusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in [4]. When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a general weak solution, and leave the general large deviation function upper bound as a conjecture.
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https://hal.archives-ouvertes.fr/hal-01465293
Contributeur : Cedric Bernardin <>
Soumis le : samedi 11 février 2017 - 15:51:42
Dernière modification le : mercredi 15 février 2017 - 01:07:00
Document(s) archivé(s) le : vendredi 12 mai 2017 - 12:42:47

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  • HAL Id : hal-01465293, version 1
  • ARXIV : 1702.03769

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Julien Barré, Cedric Bernardin, Raphaël Chetrite. Density large deviations for multidimensional stochastic hyperbolic conservation laws. 2017. <hal-01465293>

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