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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Novi Sad Journal of Mathematics, 2012, 42 (1), pp.95-116
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Contributeur : Séverine Andouze-Bernard <>
Soumis le : mardi 8 janvier 2013 - 15:43:46
Dernière modification le : mardi 8 janvier 2013 - 15:43:46

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  • HAL Id : hal-00771405, version 1

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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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