scholarly journals Survey of admissible shock waves for $2 \times 2$ systems of conservation laws with an umbilic point

2019 ◽  
Author(s):  
Fumioki Asakura ◽  
Mitsuru Yamazaki
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Umbilic Point ◽  
Systems Of Conservation Laws

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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