Existence and uniqueness of invariant measures are claimed for anisotropic degenerate parabolic-hyperbolic conservation laws driven by additive white noise, extending Debussche-Vovelle's first-order theory.
Long-time behavior, invariant measures and regularizing effects for stochastic scalar conservation laws
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study the long-time behavior and the regularity of pathwise entropy solutions to stochastic scalar conservation laws with random in time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure, and provide a rate of convergence, the latter being new even in the deterministic case for dimensions higher than two. The main tool is a new regularization result in the spirit of averaging lemmata for scalar conservation laws, which, in particular, implies a regularization by noise-type result for pathwise quasi-solutions.
fields
math.AP 1years
2019 1verdicts
REJECT 1representative citing papers
citing papers explorer
-
Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing
Existence and uniqueness of invariant measures are claimed for anisotropic degenerate parabolic-hyperbolic conservation laws driven by additive white noise, extending Debussche-Vovelle's first-order theory.