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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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Contributor : Cedric Bernardin <>
Submitted on : Tuesday, August 15, 2017 - 7:40:09 AM
Last modification on : Tuesday, May 26, 2020 - 6:50:52 PM

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Julien Barré, Cedric Bernardin, Raphaël Chetrite. Density large deviations for multidimensional stochastic hyperbolic conservation laws. Journal of Statistical Physics, Springer Verlag, 2017, Journal of Statistical Physics, 170 (3), pp.466-491. ⟨10.1007/s10955-017-1935-3⟩. ⟨hal-01465293v2⟩

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