Well-posedness by noise for scalar conservation laws

Benjamin Gess; Mario Maurelli

doi:10.1080/03605302.2018.1535604

Well-posedness by noise for scalar conservation laws

Benjamin Gess, Mario Maurelli

School of Mathematics

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

Abstract

We consider stochastic scalar conservation laws with spatially inhomogeneous flux. The regularity of the flux function with respect to its spatial variable is assumed to be low, so that entropy solutions are not necessarily unique in the corresponding deterministic scalar conservation law. We prove that perturbing the system by noise leads to well-posedness.

Original language	English
Pages (from-to)	1702-1736
Number of pages	33
Journal	Communications in partial differential equations
Volume	43
Issue number	12
DOIs	https://doi.org/10.1080/03605302.2018.1535604
Publication status	Published - 22 Mar 2019

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https://arxiv.org/abs/1701.05393

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title = "Well-posedness by noise for scalar conservation laws",

abstract = "We consider stochastic scalar conservation laws with spatially inhomogeneous flux. The regularity of the flux function with respect to its spatial variable is assumed to be low, so that entropy solutions are not necessarily unique in the corresponding deterministic scalar conservation law. We prove that perturbing the system by noise leads to well-posedness.",

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AB - We consider stochastic scalar conservation laws with spatially inhomogeneous flux. The regularity of the flux function with respect to its spatial variable is assumed to be low, so that entropy solutions are not necessarily unique in the corresponding deterministic scalar conservation law. We prove that perturbing the system by noise leads to well-posedness.

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DO - 10.1080/03605302.2018.1535604

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JO - Communications in partial differential equations

JF - Communications in partial differential equations

SN - 0360-5302

IS - 12

ER -

Well-posedness by noise for scalar conservation laws

Abstract

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