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Cheng, Hongjun; Li, Shiwei

A deposition model: Riemann problem and flux-function limits of solutions. (English) Zbl 1470.35230

Abstr. Appl. Anal. 2018, Article ID 8569435, 14 p. (2018).
Summary: The Riemann solutions of a deposition model are shown. A singular flux-function limit of the obtained Riemann solutions is considered. As a result, it is shown that the Riemann solutions of the deposition model just converge to the Riemann solutions of the limit system, the scalar conservation law with a linear flux function involving discontinuous coefficient. Especially, for some initial data, the two-shock Riemann solution of the deposition model tends to the delta-shock Riemann solution of the limit system; by contrast, for some initial data, the two-rarefaction-wave Riemann solution of the deposition model tends to the vacuum Riemann solution of the limit system. Some numerical results exhibiting the formation processes of delta-shocks and vacuum states are presented.

MSC:

35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
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