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The Random Choice Method

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Book cover Hyperbolic Conservation Laws in Continuum Physics

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 325))

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Abstract

The endeavor of solving the initial-value problem for the scalar conservation law, in Chapter VI, owes its spectacular success to the L 1 -contraction property, which applies not only to the solutions themselves but even to their approximations by means of vanishing viscosity, layering, relaxation, etc. For systems, however, the situation is different: L 1-contraction no longer applies; in its place, L 1-Lipschitz continuity will eventually be established, in Chapter XIV, albeit under substantial restrictions on the initial data. Furthermore, at the time of this writing, the requisite stability estimates have been established solely in the context of highly specialized approximating schemes that employ as building blocks the solution of the Riemann problem.

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  1. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Constantine M. Dafermos

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  1. Constantine M. Dafermos
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© 2000 Springer-Verlag Berlin Heidelberg

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Dafermos, C.M. (2000). The Random Choice Method. In: Hyperbolic Conservation Laws in Continuum Physics. Grundlehren der mathematischen Wissenschaften, vol 325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22019-1_13

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  • DOI: https://doi.org/10.1007/978-3-662-22019-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-22021-4

  • Online ISBN: 978-3-662-22019-1

  • eBook Packages: Springer Book Archive

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