# Invariant measures for stochastic conservation laws on the line

@inproceedings{Drivas2022InvariantMF, title={Invariant measures for stochastic conservation laws on the line}, author={Theodore D. Drivas and Alexander Dunlap and Cole Graham and Joonhyun La and Lenya Ryzhik}, year={2022} }

We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a unique ergodic spatially-homogeneous invariant measure for each mean in a non-explicit unbounded set. This generalizes previous work on the stochastic Burgers equation.

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