Topology of elementary waves for mixed-type systems of conservation laws

1994 ◽  
Vol 6 (3) ◽  
pp. 427-446 ◽  
Author(s):  
Dan Marchesin ◽  
C. Frederico B. Palmeira
Keyword(s):  
Conservation Laws ◽  
Mixed Type ◽  
Type Systems ◽  
Systems Of Conservation Laws ◽  
Elementary Waves

LAX SHOCKS IN MIXED-TYPE SYSTEMS OF CONSERVATION LAWS

2008 ◽  
Vol 05 (02) ◽  
pp. 295-315 ◽  
Author(s):  
ALEXEI A. MAILYBAEV ◽  
DAN MARCHESIN
Keyword(s):  
Conservation Laws ◽  
Small Amplitude ◽  
Mixed Type ◽  
Elliptic Boundary ◽  
Type Systems ◽  
Exceptional Point ◽  
Riemann Solutions ◽  
Flux Function ◽  
Systems Of Conservation Laws ◽  
Elliptic Region

Small amplitude shocks involving a state with complex characteristic speeds arise in mixed-type systems of two or more conservation laws. We study such shocks in detail in the generic case, when they appear near the codimension-1 elliptic boundary. Then we classify all exceptional codimension-2 states on smooth parts of the elliptic boundary. Asymptotic formulae describing shock curves near regular and exceptional states are derived. The type of singularity at the exceptional point depends on the second and third derivatives of the flux function. The main application is understanding the structure of small amplitude Riemann solutions where one of the initial states lies in the elliptic region.

scholarly journals On the uniqueness of solutions to hyperbolic systems of conservation laws

2021 ◽  
Vol 291 ◽  
pp. 110-153
Author(s):  
Shyam Sundar Ghoshal ◽  
Animesh Jana ◽  
Konstantinos Koumatos
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Uniqueness Of Solutions ◽  
Systems Of Conservation Laws
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