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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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