A Deposition Model: Riemann Problem and Flux-Function Limits of Solutions
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 w...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/8569435 |
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| 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. |
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| ISSN: | 1085-3375 1687-0409 |