Consider a strictly hyperbolic n×n system of conservation laws, where each characteristic field is either genuinely nonlinear or linearly degenerate. In this standard setting, it is well known that there exists a Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation. If the system admits a strictly convex entropy, we give a short proof that every entropy weak solution taking values within the domain of the semigroup coincides with a semigroup trajectory. The result shows that the assumptions of “Tame Variation” or “Tame Oscillation”, previously used to achieve uniqueness, can be removed in the presence of a strictly convex entropy.

Bressan, A., Guerra, G. (2024). Unique solutions to hyperbolic conservation laws with a strictly convex entropy. JOURNAL OF DIFFERENTIAL EQUATIONS, 387(5 April 2024), 432-447 [10.1016/j.jde.2024.01.005].

Unique solutions to hyperbolic conservation laws with a strictly convex entropy

Guerra, G
2024

Abstract

Consider a strictly hyperbolic n×n system of conservation laws, where each characteristic field is either genuinely nonlinear or linearly degenerate. In this standard setting, it is well known that there exists a Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation. If the system admits a strictly convex entropy, we give a short proof that every entropy weak solution taking values within the domain of the semigroup coincides with a semigroup trajectory. The result shows that the assumptions of “Tame Variation” or “Tame Oscillation”, previously used to achieve uniqueness, can be removed in the presence of a strictly convex entropy.
Articolo in rivista - Articolo scientifico
Systems of conservation laws; Uniqueness of entropy solutions;
English
18-gen-2024
2024
387
5 April 2024
432
447
open
Bressan, A., Guerra, G. (2024). Unique solutions to hyperbolic conservation laws with a strictly convex entropy. JOURNAL OF DIFFERENTIAL EQUATIONS, 387(5 April 2024), 432-447 [10.1016/j.jde.2024.01.005].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/456882
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