Non-standard Shocks in the Buckley-Leverett Equation (CROSBI ID 220967)
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Podaci o odgovornosti
Kalisch, Henrik ; Mitrović, Darko ; Nordbotten, Jan
engleski
Non-standard Shocks in the Buckley-Leverett Equation
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.
non-standard shocks; Buckley-Leveret equations
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Podaci o izdanju
428 (2)
2015.
882-895
objavljeno
0022-247X
10.1016/j.jmaa.2015.03.041