scholarly journals A limiting viscosity approach to Riemann solutions containing delta-shock waves for nonstrictly hyperbolic conservation laws

1997 ◽  
Vol 55 (2) ◽  
pp. 361-373 ◽  
Author(s):  
Jiaxin Hu
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Riemann Solutions ◽  
Hyperbolic Conservation ◽  
Delta Shock ◽  
Delta Shock Waves

scholarly journals Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Hongjun Cheng
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Hyperbolic System ◽  
Delta Shock Wave ◽  
Riemann Solutions ◽  
Delta Shock ◽  
System Of Conservation Laws ◽  
Elementary Waves ◽  
Delta Shock Waves ◽  
Linearly Degenerate

This paper is devoted to the study of delta shock waves for a hyperbolic system of conservation laws of Keyfitz-Kranzer type with two linearly degenerate characteristics. The Riemann problem is solved constructively. The Riemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solution are established. These analytical results match well the numerical ones. Finally, two kinds of interactions of elementary waves are discussed.

scholarly journals Symmetries of conservation laws

2005 ◽  
Vol 77 (91) ◽  
pp. 29-51
Author(s):  
Sanja Konjik
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Gas Dynamics ◽  
Hyperbolic Conservation Laws ◽  
Strong Association ◽  
Group Analysis ◽  
Symmetry Groups ◽  
Dynamics Model ◽  
Hyperbolic Conservation ◽  
Systems Of Conservation Laws

We apply techniques of symmetry group analysis in solving two systems of conservation laws: a model of two strictly hyperbolic conservation laws and a zero pressure gas dynamics model, which both have no global solution, but whose solution consists of singular shock waves. We show that these shock waves are solutions in the sense of 1-strong association. Also, we compute all project able symmetry groups and show that they are 1-strongly associated, hence transform existing solutions in the sense of 1-strong association into other solutions.

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