A Degenerate Parabolic-Hyperbolic System Modeling the Spreading of Surfactants

1997 ◽  
Vol 28 (5) ◽  
pp. 1048-1063 ◽  
Author(s):  
Michael Renardy
Keyword(s):  
Hyperbolic System ◽  
System Modeling ◽  
Degenerate Parabolic

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.

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