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Riemann problem for a \(2\times2\) system of balance laws through approximate Lie symmetries. (English) Zbl 1242.35166

Greco, A. M. (ed.) et al., Proceedings “WASCOM 2009”. 15th conference on waves and stability in continuous media, Palermo, Italy, June 28–July 1, 2009. Hackensack, NJ: World Scientific (ISBN 978-981-4317-41-2/hbk; 978-981-4317-42-9/ebook). 103-108 (2010).
Summary: We present an approach, based on the approximate Lie symmetries, for solving a Riemann problem for a \(2 \times 2\) system of balance laws. Focusing the attention on the approximate Lie symmetries which perturbe the homogeneous time and space scaling (admitted by every system of conservation laws), we are able to determine approximate invariant solutions suitable to describe generalized rarefaction waves.
For the entire collection see [Zbl 1237.35006].

MSC:

35L65 Hyperbolic conservation laws
35B06 Symmetries, invariants, etc. in context of PDEs
35L67 Shocks and singularities for hyperbolic equations
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