Invariant measures for stochastic conservation laws on the line
Probability
2023-08-29 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2201.12641,
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},
journal= {arXiv preprint arXiv:2201.12641},
year = {2023}
}
Comments
33 pages; generalized assumptions on the noise in this version