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Genuinely Nonlinear Scalar Conservation Laws

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Hyperbolic Conservation Laws in Continuum Physics

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

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Abstract

Despite its apparent simplicity, the genuinely nonlinear scalar conservation law in one-space dimension possesses a surprisingly rich theory, which deserves attention, not only for its intrinsic interest, but also because it provides valuable insight in the behavior of systems. The discussion here will employ the theory of generalized characteristics developed in Chapter X. From the standpoint of this approach, the special feature of genuinely nonlinear scalar conservation laws is that the extremal backward generalized characteristics are essentially classical characteristics, that is straight lines along which the solution is constant. This property induces such a heavy constrain that one is able to derive very precise information on regularity and large time behavior of solutions.

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

    Constantine M. Dafermos

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Dafermos, C.M. (2000). Genuinely Nonlinear Scalar Conservation Laws. 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_11

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  • DOI: https://doi.org/10.1007/978-3-662-22019-1_11

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