Ergodicity for Stochastic Conservation Laws with Multiplicative Noise

Zhao Dong; Rangrang Zhang; Tusheng Zhang

doi:10.1007/s00220-022-04629-x

Ergodicity for Stochastic Conservation Laws with Multiplicative Noise

Zhao Dong, Rangrang Zhang^*, Tusheng Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

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

Abstract

We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in the setting of kinetic solutions taking values in an L¹-weighted space.

Original language	English
Pages (from-to)	1739-1789
Number of pages	51
Journal	Communications in Mathematical Physics
Volume	400
Issue number	3
DOIs	https://doi.org/10.1007/s00220-022-04629-x
Publication status	Published - Jun 2023

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title = "Ergodicity for Stochastic Conservation Laws with Multiplicative Noise",

abstract = "We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in the setting of kinetic solutions taking values in an L1-weighted space.",

author = "Zhao Dong and Rangrang Zhang and Tusheng Zhang",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s00220-022-04629-x",

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AB - We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in the setting of kinetic solutions taking values in an L1-weighted space.

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Ergodicity for Stochastic Conservation Laws with Multiplicative Noise

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