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Mathematics > Analysis of PDEs

arXiv:1509.08273 (math)
[Submitted on 28 Sep 2015 (v1), last revised 1 Mar 2016 (this version, v2)]

Title:Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness

Authors:Graziano Crasta, Virginia De Cicco, Guido De Philippis, Francesco Ghiraldin
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Abstract:We investigate the structure of solutions of conservation laws with discontinuous flux under quite general assumption on the flux. We show that any entropy solution admits traces on the discontinuity set of the coefficients and we use this to prove the validity of a generalized Kato inequality for any pair of solutions. Applications to uniqueness of solutions are then given.
Comments: 20 pages in Arch. Rational Mech. Anal. (2016) - online first
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35L65
Report number: Roma01.Math.AP
Cite as: arXiv:1509.08273 [math.AP]
  (or arXiv:1509.08273v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1509.08273
Journal reference: Arch. Ration. Mech. Anal. 221 (2016), pp. 961-985
Related DOI: https://doi.org/10.1007/s00205-016-0976-0

Submission history

From: Graziano Crasta [view email]
[v1] Mon, 28 Sep 2015 11:17:45 UTC (25 KB)
[v2] Tue, 1 Mar 2016 07:24:35 UTC (25 KB)
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