Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Remarks on the theory of the divergence-measure fields

Author: Hermano Frid
Journal: Quart. Appl. Math. 70 (2012), 579-596
MSC (2010): Primary 26B20, 28C05, 35L65, 35B35; Secondary 26B35, 26B12, 35L67
DOI: https://doi.org/10.1090/S0033-569X-2012-01311-5
Published electronically: May 9, 2012
MathSciNet review: 2986135
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Abstract: We review the theory of the (extended) divergence-measure fields providing an up-to-date account of its basic results established by Chen and Frid (1999, 2002), as well as the more recent important contributions by Silhavý (2008, 2009). We include a discussion on some pairings that are important in connection with the definition of normal trace for divergence-measure fields. We also review its application to the uniqueness of Riemann solutions to the Euler equations in gas dynamics, as given by Chen and Frid (2002). While reviewing the theory, we simplify a number of proofs allowing an almost self-contained exposition.

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Additional Information

Hermano Frid
Affiliation: Instituto de Matemática Pura e Aplicada - IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, RJ 22460-320, Brazil
Email: hermano@impa.br

DOI: https://doi.org/10.1090/S0033-569X-2012-01311-5
Keywords: Divergence-measure fields, normal traces, Gauss-Green theorem, product rule
Received by editor(s): January 9, 2012
Published electronically: May 9, 2012
Dedicated: Dedicated to Costas Dafermos on his 70th birthday
Article copyright: © Copyright 2012 Brown University

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