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Multidimensional conservation laws: overview, problems, and perspective. (English) Zbl 1257.35122

Bressan, Alberto (ed.) et al., Nonlinear conservation laws and applications. Proceedings of the summer program, IMA, Minneapolis, MN, USA, July 13–31, 2009. New York, NY: Springer (ISBN 978-1-4419-9553-7; 978-1-4419-9554-4/ebook). The IMA Volumes in Mathematics and its Applications 153, 23-72 (2011).
This article presents some basic features and phenomena associated with multi-dimensional (MD) hyperbolic conservation laws. Important developments made in the recent decades have been highlighted, and certain models and related problems have been presented with approaches used therein. Some recent developments with analysis of MD steady supersonic and transonic problems have been discussed. Shock reflection-diffraction and self-similar solution have been formulated. A theory of divergence measure fields towards the analysis of entropy solutions is discussed.
For the entire collection see [Zbl 1214.35003].

MSC:

35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35Q31 Euler equations
34A35 Ordinary differential equations of infinite order
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References:

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