Abstract
The theory of the scalar balance law, in several spatial dimensions, has reached a state of virtual completeness. In the framework of classical solutions, the elementary, yet effective, method of characteristics yields a sharper version of Theorem 5.1.1, determining explicitly the life span of solutions with Lipschitz continuous initial data and thereby demonstrating that in general this life span is finite. Thus one must deal with weak solutions, even when the initial data are very smooth.
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© 2016 Springer-Verlag Berlin Heidelberg
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Dafermos, C.M. (2016). The \(L^1\) Theory for Scalar Conservation Laws. In: Hyperbolic Conservation Laws in Continuum Physics. Grundlehren der mathematischen Wissenschaften. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49451-6_6
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DOI: https://doi.org/10.1007/978-3-662-49451-6_6
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-662-49451-6
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