Hugoniot–Maslov chains of a shock wave in conservation law with polynomial flow

✍ Scribed by Panters Rodríguez Bermúdez; Baldomero Valiño Alonso

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 128 KB
• Volume: 280
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200410523

✦ Synopsis

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)