Naslov
Non-standard Shocks in the Buckley-Leverett Equation, Journal of Mathematical Analysis and Applications
(Non-standard Shocks in the Buckley-Leverett Equation)

Autori
Kalisch, Henrik ; Mitrović, Darko ; Nordbotten, Jan

Izvornik
Journal of mathematical analysis and applications (0022-247X) 428 (2015), 2; 882-895

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
non-standard shocks; Buckley-Leveret equations

Sažetak
It is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct non-monotone solutions of the Buckley–Leverett equation. These solutions are interpreted using a recent variational definition of delta shock waves in which the Rankine–Hugoniot deficit is explicitly accounted for. The delta shock waves are also limits of approximate solutions constructed using a recent extension of the weak asymptotic method to complex-valued approximations. Finally, it is shown how these non-standard shocks can be fitted together to construct similarity and traveling-wave solutions which are non-monotone, but still admissible in the sense that characteristics either enter or are parallel to the shock trajectories.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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