Abstract
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.
Mathematics Subject Classification (2010). Primary 35L65; Secondary 35L67, 76L05.
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Shelkovich, V.M. (2013). Concept of Delta-shock Type Solutions to Systems of Conservation Laws and the Rankine–Hugoniot Conditions. In: Molahajloo, S., Pilipović, S., Toft, J., Wong, M. (eds) Pseudo-Differential Operators, Generalized Functions and Asymptotics. Operator Theory: Advances and Applications, vol 231. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0585-8_16
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DOI: https://doi.org/10.1007/978-3-0348-0585-8_16
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