<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We investigate the existence of the solution of the Riemann Problem for a simplified water ow model on a vegetated surface - system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous topography and discontinuous porosity is also non-conservative. In order to define Riemann solution for such systems, it is necessary to introduce a family of paths that connects the states defining the Riemann Problem. We focus our attention towards choosing such a family based on physical arguments. We provide the structure of the solution for such Riemann Problems.</p></abstract>

We investigate the existence of the solution of the Riemann Problem for a simplified water ow model on a vegetated surface - system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous topography and discontinuous porosity is also non-conservative. In order to define Riemann solution for such systems, it is necessary to introduce a family of paths that connects the states defining the Riemann Problem. We focus our attention towards choosing such a family based on physical arguments. We provide the structure of the solution for such Riemann Problems.

Riemann Problem for Shallow Water Equation with Vegetation

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Riemann Problem for Shallow Water Equation with Vegetation"}

We investigate the existence of the solution of the Riemann Problem for a simplified water ow model on a vegetated surface - system of shallow water type...

Riemann Problem for Shallow Water Equation with Vegetation

Published Online: Nov 22, 2018

Page range: 145 - 173

Received: Dec 01, 2016

Accepted: Jun 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0023

Keywords
hyperbolic nonconservativ law, measure solutions, path connectig, shock waves

© 2018 Stelian Ion, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Riemann Problem for Shallow Water Equation with Vegetation

Published Online: Nov 22, 2018

Page range: 145 - 173

Received: Dec 01, 2016

Accepted: Jun 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0023

Keywordshyperbolic nonconservativ law, measure solutions, path connectig, shock waves

© 2018 Stelian Ion, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
hyperbolic nonconservativ law, measure solutions, path connectig, shock waves