Remarks on the theory of the divergencemeasure fields
Author:
Hermano Frid
Journal:
Quart. Appl. Math. 70 (2012), 579596
MSC (2010):
Primary 26B20, 28C05, 35L65, 35B35; Secondary 26B35, 26B12, 35L67
Published electronically:
May 9, 2012
MathSciNet review:
2986135
Fulltext PDF
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Abstract: We review the theory of the (extended) divergencemeasure fields providing an uptodate 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 divergencemeasure 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 selfcontained 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 22460320, Brazil
Email:
hermano@impa.br
DOI:
http://dx.doi.org/10.1090/S0033569X2012013115
PII:
S 0033569X(2012)013115
Keywords:
Divergencemeasure fields,
normal traces,
GaussGreen 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
