Hugoniot–Maslov chains of a shock wave in conservation law with polynomial flow |
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| Authors: | Panters Rodríguez Bermúdez Baldomero Valiño Alonso |
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| Institution: | 1. Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, CEP 22460‐320 Rio de Janeiro, BrazilPhone: +55 21 2529 5231, Fax: +55 21 2529 5075;2. Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, CP 10400, Cuba;3. Phone: +537 870 43 67, Fax: +537 873 63 10 |
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| Abstract: | In this paper we give a theoretical foundation to the asymptotical development proposed by V. P. Maslov for shock type singular solutions of conservations laws, in the framework of Colombeau theory of generalized functions. Indeed, operating with Colombeau differential algebra of simplified generalized functions, we proof that Hugoniot–Maslov chains are necessary conditions for the existence of shock waves in conservation laws with polynomial flows. As a particular case, these equations include the Hugoniot–Maslov chains for shock waves in the Hopf equation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Colombeau algebras of generalized functions conservation laws shock waves Hugoniot− Maslov chains |
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