A Deposition Model: Riemann Problem and Flux-Function Limits of Solutions

Hongjun Cheng and Shiwei Li

Abstract and Applied Analysis, 2018, vol. 2018, 1-14

Abstract:

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:8569435

DOI: 10.1155/2018/8569435

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