Abstract
The theory of the Cauchy problem for hyperbolic conservation laws is confronted with two major challenges. First, classical solutions, starting out from smooth initial values, spontaneously develop discontinuities; hence, in general, only weak solutions may exist in the large. Next, weak solutions to the Cauchy problem fail to be unique. One does not have to dig too deep in order to encounter these difficulties.
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© 2016 Springer-Verlag Berlin Heidelberg
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Dafermos, C.M. (2016). The Cauchy Problem. In: Hyperbolic Conservation Laws in Continuum Physics. Grundlehren der mathematischen Wissenschaften. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49451-6_4
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DOI: https://doi.org/10.1007/978-3-662-49451-6_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-49449-3
Online ISBN: 978-3-662-49451-6
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