<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “small enough”). One di culty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another di culty is given by the fact that the construction of the solution assumes solving an equation which has no global solution. Finally, we present some cases to illustrate the existence and non-existence of the solution.</p></abstract>

We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “small enough”). One di culty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another di culty is given by the fact that the construction of the solution assumes solving an equation which has no global solution. Finally, we present some cases to illustrate the existence and non-existence of the solution.

Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the...

Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

Published Online: Sep 22, 2020

Page range: 93 - 114

Received: Jul 10, 2019

Accepted: Dec 16, 2019

DOI: https://doi.org/10.2478/auom-2020-0021

Keywords
hyperbolic nonconservative law, dam-break, elementary waves, composite waves

© 2020 Stelian Ion et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

Published Online: Sep 22, 2020

Page range: 93 - 114

Received: Jul 10, 2019

Accepted: Dec 16, 2019

DOI: https://doi.org/10.2478/auom-2020-0021

Keywordshyperbolic nonconservative law, dam-break, elementary waves, composite waves

© 2020 Stelian Ion et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
hyperbolic nonconservative law, dam-break, elementary waves, composite waves