no. G3
Équations aux dérivées partielles
On optimal regularity estimates for finite-entropy solutions of scalar conservation laws
Lamy, Xavier1  ; Lorent, Andrew2 ; Peng, Guanying3
1Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPSIMT, F-31062 Toulouse Cedex 9, France.
2Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA.
3Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA.
Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 599-608

We consider finite-entropy solutions of scalar conservation laws u t +a(u) x =0, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function a is strictly convex (with possibly degenerate convexity) and a ′′ forms a doubling measure, we obtain a characterization of finite-entropy solutions in terms of an optimal regularity estimate involving a cost function first used by Golse and Perthame.

Reçu le :
Accepté le :
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DOI : 10.5802/crmath.427
Classification : 35L65

Lamy, Xavier  1   ; Lorent, Andrew  2   ; Peng, Guanying  3

1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPSIMT, F-31062 Toulouse Cedex 9, France.
2 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA.
3 Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Lamy, Xavier; Lorent, Andrew; Peng, Guanying. On optimal regularity estimates for finite-entropy solutions of scalar conservation laws. Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 599-608. doi: 10.5802/crmath.427

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