On the theory of divergence-measure fields and its applications

Journal article

Divergence-measure fields are extended vector fields, including vector fields in Lp and vector-valued Radon measures, whose divergences are Radon measures. Such fields arise naturally in the study of entropy solutions of nonlinear conservation laws and other areas. In this paper, a theory of divergence-measure fields is presented and analyzed, in which normal traces, a generalized Gauss-Green theorem, and product rules, among others, are established. Some applications of this theory to severa...

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Authors: Chen, G; Frid, H

• Journal: Bulletin of the Brazilian Mathematical Society
• Volume: 32
• Issue: 3
• Pages: 401-433
• Publication date: 2001-01-01
• DOI: 10.1007/BF01233674
• EISSN: 1678-7714
• ISSN: 0100-3569
• Language: English
• Keywords: Entropy inequality; Normal traces; Divergence-measure fields; Stability; Product rules; Entropy solutions; Gas dynamics; Cauchy problem; Euler equations; Boundary layers; Initial layers; Uniqueness; Gauss-Green theorem; Vacuum; Conservation laws; Radon measures