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DOE OSTI · 22784015

Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws

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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. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31–45, 2010). 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 more general weak solution, and leave the general large deviation function upper bound as a conjecture.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTINGCONSERVATION LAWSDENSITYFUNCTIONSMATHEMATICAL SOLUTIONSMATRICESSTOCHASTIC PROCESSESVISCOSITY

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2018-02-15. Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws. https://doi.org/10.1007/s10955-017-1935-3

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