Invariant measures for stochastic conservation laws on the line

Theodore D. Drivas; Alexander Dunlap; Cole Graham; Joonhyun La; Lenya Ryzhik

doi:10.1088/1361-6544/acdb3a

Invariant measures for stochastic conservation laws on the line

Theodore D. Drivas
, Alexander Dunlap
, Cole Graham
, Joonhyun La
, Lenya Ryzhik

Mathematics

New York University
Duke University
Brown University
Imperial College London
Stanford University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 generalises previous work on the stochastic Burgers equation.

Original language	English
Pages (from-to)	4553-4594
Number of pages	42
Journal	Nonlinearity
Volume	36
Issue number	9
DOIs	https://doi.org/10.1088/1361-6544/acdb3a
State	Published - Sep 1 2023

Keywords

35R60
37L40
37L55
60H15
invariant measures
kick forcing
stochastic conservation laws

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10.1088/1361-6544/acdb3a

Cite this

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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 generalises previous work on the stochastic Burgers equation.",

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AU - Dunlap, Alexander

AU - Graham, Cole

AU - La, Joonhyun

AU - Ryzhik, Lenya

PY - 2023/9/1

Y1 - 2023/9/1

N2 - 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 generalises previous work on the stochastic Burgers equation.

AB - 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 generalises previous work on the stochastic Burgers equation.

KW - 35R60

KW - 37L40

KW - 37L55

KW - 60H15

KW - invariant measures

KW - kick forcing

KW - stochastic conservation laws

UR - https://www.scopus.com/pages/publications/85165891033

U2 - 10.1088/1361-6544/acdb3a

DO - 10.1088/1361-6544/acdb3a

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VL - 36

SP - 4553

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JO - Nonlinearity

JF - Nonlinearity

IS - 9

ER -

Invariant measures for stochastic conservation laws on the line

Abstract

Keywords

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