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Two-dimensional shock waves for a model problem. (English. Russian original) Zbl 1406.35294

Math. Notes 103, No. 6, 936-942 (2018); translation from Mat. Zametki 103, No. 6, 875-883 (2018).
The author studies the Riemann’ problem for the two-component modification of the system of shallow water equations, which is nonstrictly hyperbolic in the sense of Petrovskii but is not nonstrictly hyperbolic in the sense of Lax. The author shows the existence of a two-velocity regime which is essentially the two-dimensional shock wave. The author’s study shows that the appearance of an associated vector leads to the Riemann-Hugoniot catastrophe, and the two-velocity regime propagates in the eigenspace corresponding to the multiple eigenvalue.
Reviewer: Cheng He (Beijing)

MSC:

35Q35 PDEs in connection with fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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