scholarly journals Riemann problem for a non-strictly hyperbolic system in chemotaxis

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tong Li ◽  
Nitesh Mathur
Keyword(s):  
Riemann Problem ◽  
Hyperbolic System

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

2020 ◽  
Vol 28 (2) ◽  
pp. 93-114
Author(s):  
Stelian Ion ◽  
Stefan-Gicu Cruceanu ◽  
Dorin Marinescu
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Global Solution ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Shallow Water Equations ◽  
Local Existence ◽  
Water Model ◽  
Constructive Approach ◽  
Shallow Water Model

AbstractWe 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.

scholarly journals Admissibility conditions for Riemann data in shallow water theory

2020 ◽  
Vol 75 (7) ◽  
pp. 637-648
Author(s):  
Martin O. Paulsen ◽  
Henrik Kalisch
Keyword(s):  
Shallow Water ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Shallow Water Equations ◽  
System Modeling ◽  
Water System ◽  
Shallow Water Theory ◽  
Constant Depth ◽  
Shallow Water System ◽  
Reasonable Sense

AbstractConsideration is given to the shallow-water equations, a hyperbolic system modeling the propagation of long waves at the surface of an incompressible inviscible fluid of constant depth. It is well known that the solution of the Riemann problem associated to this system may feature dry states for some configurations of the Riemann data. This article will discuss various scenarios in which the Riemann problem for the shallow water system arises in a physically reasonable sense. In particular, it will be shown that if certain physical assumptions on the disposition of the Riemann data are made, then dry states can be avoided in the solution of the Riemann problem.

scholarly journals The Perturbed Riemann Problem with Delta Shock for a Hyperbolic System

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Xinli Han ◽  
Lijun Pan
Keyword(s):  
Initial Data ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Contact Discontinuity ◽  
Riemann Problems ◽  
Delta Shock ◽  
Riemann Solution ◽  
Internal Mechanism

In this paper, we study the perturbed Riemann problem with delta shock for a hyperbolic system. The problem is different from the previous perturbed Riemann problems which have no delta shock. The solutions to the problem are obtained constructively. From the solutions, we see that a delta shock in the corresponding Riemann solution may turn into a shock and a contact discontinuity under a perturbation of the Riemann initial data. This shows the instability and the internal mechanism of a delta shock. Furthermore, we find that the Riemann solution of the hyperbolic system is instable under this perturbation, which is also quite different from the previous perturbed Riemann problems.

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