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Large deviations for stochastic conservation laws

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A class of viscid, fully nonlinear conservation laws is considered. Large deviations for the laws of the solution are investigated, in the limit of jointly vanishing noise and viscosity. In the first part I will review the case of elliptical second-order viscosity. Next, more recent advances for nonlinear fractional viscosities will be addressed.

The rate functionals obtained provide a notion of ‘entropy’ for solutions to inviscid conservation laws.

This talk is part of the Isaac Newton Institute Seminar Series series.

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