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

Access to Document

10.1007/s00205-016-0976-0

Cite this

@article{e2de28d4873c45fe97f25055d19d17b1,

title = "Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness",

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.",

author = "Graziano Crasta and {De Cicco}, Virginia and {De Philippis}, Guido and Francesco Ghiraldin",

note = "Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",

year = "2016",

month = aug,

day = "1",

doi = "10.1007/s00205-016-0976-0",

language = "English (US)",

volume = "221",

pages = "961--985",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness

AU - Crasta, Graziano

AU - De Cicco, Virginia

AU - De Philippis, Guido

AU - Ghiraldin, Francesco

PY - 2016/8/1

Y1 - 2016/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84959091589&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959091589&partnerID=8YFLogxK

U2 - 10.1007/s00205-016-0976-0

DO - 10.1007/s00205-016-0976-0

M3 - Article

AN - SCOPUS:84959091589

VL - 221

SP - 961

EP - 985

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this