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

Hongjun Cheng and Shiwei Li

Abstract and Applied Analysis, 2018, vol. 2018, issue 1

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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https://doi.org/10.1155/2018/8569435

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:8569435

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