Abstract
In this first chapter on systems we explicitly construct the classical and the nonclassical entropy solutions to the Riemann problem associated with a strictly hyperbolic system of conservation laws. The initial data consist of single jump discontinuities of sufficiently small strength. As was already observed with scalar conservation laws (Chapter II), solutions can be obtained by combining shock waves and rarefaction waves together. Motivated by the applications (Sections I-3 and I-4) we are primarily interested in systems endowed with a strictly convex entropy pair and in solutions satisfying a single entropy inequality.
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© 2002 Springer Basel AG
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LeFloch, P.G. (2002). The Riemann Problem. In: Hyperbolic Systems of Conservation Laws. Lectures in Mathematics. ETH Zürich. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8150-0_6
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DOI: https://doi.org/10.1007/978-3-0348-8150-0_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6687-2
Online ISBN: 978-3-0348-8150-0
eBook Packages: Springer Book Archive