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The Rankine-Hugoniot conditions and balance laws for \(\delta \) -shocks. (English) Zbl 1151.35400
J. Math. Sci., New York 151, No. 1, 2781-2792 (2008); translation from Fundam. Prikl. Mat. 12, No. 6, 213-229 (2006).
Summary: New definitions of \(\delta \)-shock-wave-type solutions are introduced for two (one-dimensional) types of hyperbolic systems of conservation laws. The corresponding Rankine-Hugoniot conditions for \(\delta \)-shocks are derived and their geometrical interpretation is given. Balance laws connected with “area” mass and momentum transportation for \(\delta \)-shocks are derived.

MSC:
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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