Geodesic
The Rankine--Hugoniot conditions and balance laws for $\delta$-shocks
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 213-229

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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. 
@article{FPM_2006_12_6_a12,
     author = {V. M. Shelkovich},
     title = {The {Rankine--Hugoniot} conditions and balance laws for $\delta$-shocks},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {213--229},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a12/}
}
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V. M. Shelkovich. The Rankine--Hugoniot conditions and balance laws for $\delta$-shocks. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 213-229. http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a12/