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Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica “G. Castelnuovo”, Univ. di Roma I, P.le A. Moro 2, 00185, Rome, Italy

    Graziano Crasta

  2. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Univ. di Roma I, Via A. Scarpa 10, 00185, Rome, Italy

    Virginia De Cicco

  3. Unité de Mathématiques Pure et Appliquées-ENS de Lyon, 46 Allée d’Italie, 69364, Lyon Cedex 07, France

    Guido De Philippis

  4. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Francesco Ghiraldin

Authors
  1. Graziano Crasta
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  2. Virginia De Cicco
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  3. Guido De Philippis
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  4. Francesco Ghiraldin
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Correspondence to Graziano Crasta.

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Communicated by A. Bressan

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Crasta, G., De Cicco, V., De Philippis, G. et al. Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness. Arch Rational Mech Anal 221, 961–985 (2016). https://doi.org/10.1007/s00205-016-0976-0

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  • DOI: https://doi.org/10.1007/s00205-016-0976-0

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