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

Graziano Crasta; Virginia De Cicco; Guido De Philippis; Francesco Ghiraldin

doi:10.1007/s00205-016-0976-0

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

Graziano Crasta, Virginia De Cicco, Guido De Philippis, Francesco Ghiraldin

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	961-985
Number of pages	25
Journal	Archive for Rational Mechanics and Analysis
Volume	221
Issue number	2
DOIs	https://doi.org/10.1007/s00205-016-0976-0
State	Published - Aug 1 2016

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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

Abstract

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