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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Journal of Statistical Physics, Springer Verlag, 2017, Journal of Statistical Physics, 170 (3), pp.466-491. 〈https://link.springer.com/article/10.1007/s10955-017-1935-3#citeas〉. 〈10.1007/s10955-017-1935-3〉
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Soumis le : mardi 15 août 2017 - 07:40:09
Dernière modification le : jeudi 3 mai 2018 - 15:32:07

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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. 〈https://link.springer.com/article/10.1007/s10955-017-1935-3#citeas〉. 〈10.1007/s10955-017-1935-3〉. 〈hal-01465293v2〉

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