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Quasilinear Hyperbolic Systems with Involutions

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Analysis and Continuum Mechanics

Abstract

The evolution of n-dimensional continuous media with elastic response is generally governed by quasilinear hyperbolic systems of partial differential equations

$${artial _t}U + umimits_{lpha = 1}^m {{artial _lpha }} {G_lpha }(U) = 0$$
(1.1)

which may express, as applicable, the conservation laws of mass, momentum, energy, electric charge, etc. Here x takes values in R m and ∂ α stands for the operator ∂/∂x α The state vector U takes values in an open subset O of R n and

$${G_lpha }:arphi o {R^n},{ext{ }}lpha {ext{ = 1,}} dots ,m,$$
(1.2)

are given, smooth, constitutive functions.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, Rhode Island, USA

    Constantine M. Dafermos

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  1. Constantine M. Dafermos
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Dedicated to James Serrin on his sixtieth birthday

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© 1989 Springer-Verlag Berlin Heidelberg

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Dafermos, C.M. (1989). Quasilinear Hyperbolic Systems with Involutions. In: Analysis and Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83743-2_16

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  • DOI: https://doi.org/10.1007/978-3-642-83743-2_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50917-2

  • Online ISBN: 978-3-642-83743-2

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