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Published in:
2013 | OriginalPaper | Chapter
Concept of Delta-shock Type Solutions to Systems of Conservation Laws and the Rankine–Hugoniot Conditions
Author : V. M. Shelkovich
Published in: Pseudo-Differential Operators, Generalized Functions and Asymptotics
Publisher: Springer Basel
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To solve nonlinear systems of conservation laws, we need a proper concept of weak solution. The aim of this paper is to explain how to derive integral identities for defining
δ
-shock type solutions in the sense of Schwartzian distributions. We consider two types of systems to compare our definitions. System (1.3) is a standard system admitting delta-shocks and our definition is given by the identities (2.9). System (3.1) is non-typical, and in addition to the identities (3.8), we need to use relation (3.7). We restrict ourselves to the consideration of
δ
-shocks concentrated only on the surface of codimension 1. Our approach can be used to derive integral identities for other type systems.