Obtaining shock solutions via Maslov's theory and Colombeau's algebra for conservation laws with analytical coefficients

Abstract : In this paper, via the algebra of generalized functions, we investigate the generalized Riemann's problem associated to conservation laws with analytical coefficients. This allows us to transform the problem into a system of ordinary differential equations. In some particular cases, such that Burgers' and conservative Richard's equation, approximated solutions are obtained by the truncation of the so called Hugoniot-Maslov's chain and numerical simulations are also presented in the case of equations with polynomial coefficients.
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Contributor : Séverine Andouze-Bernard <>
Submitted on : Tuesday, January 8, 2013 - 3:43:46 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:27 PM

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Séverine Andouze-Bernard, Alex Méril, P. Rodriguez-Bermudez, B. Valino-Alonso. Obtaining shock solutions via Maslov's theory and Colombeau's algebra for conservation laws with analytical coefficients. Novi Sad Journal of Mathematics, 2012, 42 (1), pp.95-116. 〈hal-00771405〉

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