The Rankine--Hugoniot conditions and balance laws for $\delta$-shocks

V. M. Shelkovich

Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 213-229.

Résumé

New definitions of $\delta$-shock wave-type solutions are introduced for two (one-dimensional) types of hyperbolic systems of conservation laws. 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.

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