Hyperbolic systems of conversion laws 20.05.21.pdf (435.57 kB)
On the uniqueness of solutions to hyperbolic systems of conservation laws
journal contribution
posted on 2023-06-09, 23:55 authored by Shyam Sundar Ghoshal, Animesh Jana, Konstantinos KoumatosKonstantinos KoumatosFor general hyperbolic systems of conservation laws we show that dissipative weak solutions belonging to an appropriate Besov space B and satisfying a one-sided bound condition are unique within the class of dissipative solutions. The exponent a>1/2 is universal independently of the nature of the nonlinearity and the Besov regularity need only be imposed in space when the system is expressed in appropriate variables. The proof utilises a commutator estimate which allows for an extension of the relative entropy method to the required regularity setting. The systems of elasticity, shallow water magnetohydrodynamics, and isentropic Euler are investigated, recovering recent results for the latter. Moreover, the article explores a triangular system motivated by studies in chromatography and constructs an explicit solution which fails to be Lipschitz, yet satisfies the conditions of the presented uniqueness result. q a,8
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Publication status
- Published
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- Accepted version
Journal
Journal of Differential EquationsISSN
0022-0396Publisher
ElsevierExternal DOI
Volume
291Page range
110-153Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-05-21First Open Access (FOA) Date
2022-05-11First Compliant Deposit (FCD) Date
2021-05-20Usage metrics
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