Obtaining shock solutions via Maslov's theory and Colombeau's algebra for conservation laws with analytical coefficients - Archive ouverte HAL
Article Dans Une Revue Novi Sad Journal of Mathematics Année : 2012

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

Alex Méril
  • Fonction : Auteur
  • PersonId : 934947
P. Rodriguez-Bermudez
  • Fonction : Auteur
  • PersonId : 934948
B. Valino-Alonso
  • Fonction : Auteur
  • PersonId : 934949

Résumé

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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Dates et versions

hal-00771405 , version 1 (08-01-2013)

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  • HAL Id : hal-00771405 , version 1

Citer

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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