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Measure-theoretic analysis and nonlinear conservation laws

Abstract:

We discuss some recent developments and trends of applying measure-theoretic analysis to the study of nonlinear conservation laws. We focus particularly on entropy solutions without bounded variation and Cauchy fluxes on oriented surfaces which are used to formulate the balance law. Our analysis employs the Gauss-Green formula and normal traces for divergence-measure fields, Young measures and compensated compact ness, blow-up and scaling techniques, entropy methods, and related measure-theor...

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Journal:
Pure and Applied Mathematics Quarterly
Volume:
3
Issue:
3
Pages:
841-879
Publication date:
2007-01-01
EISSN:
1558-8602
ISSN:
1558-8599

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