scholarly journals Hyperbolicity and genuine nonlinearity conditions for certain p-systems of conservation laws, week solutions and the entropy condition

2017 ◽  
Vol 35 (1) ◽  
pp. 11-36
Author(s):  
Edgardo Pérez ◽  
◽  
Krzysztof Rózga ◽  
Keyword(s):  
Conservation Laws ◽  
P Systems ◽  
Entropy Condition ◽  
Systems Of Conservation Laws ◽  
Genuine Nonlinearity

scholarly journals Resonance in rarefaction and shock curves: Local analysis and numerics of the continuation method

2020 ◽  
Vol 17 (04) ◽  
pp. 639-676
Author(s):  
A. C. Alvarez ◽  
G. T. Goedert ◽  
D. Marchesin
Keyword(s):  
Conservation Laws ◽  
Continuation Method ◽  
Local Analysis ◽  
Jordan Chain ◽  
Numerical Examples ◽  
Composite Field ◽  
Systems Of Conservation Laws ◽  
Non Local ◽  
Composite Wave ◽  
Genuine Nonlinearity

We describe certain crucial steps in the development of an algorithm for finding the Riemann solution to systems of conservation laws. We relax the classical hypotheses of strict hyperbolicity and genuine nonlinearity due to Lax. First, we present a procedure for continuing wave curves beyond points where characteristic speeds coincide, i.e. at wave curve points of maximal co-dimensionality. This procedure requires strict hyperbolicity on both sides of the coincidence locus. Loss of strict hyperbolicity is regularized by means of a Generalized Jordan Chain, which serves to construct a four-fold sub-manifold structure on which wave curves can be continued. Second, we analyze the loss of genuine nonlinearity. We prove a new result: the existence of composite wave curves when the composite wave traverses either the inflection locus or an anomalous part of the non-local composite wave curve. In this sense, we find conditions under which the composite field is well defined and its singularities can be removed, allowing use of our continuation method. Finally, we present numerical examples for a non-strictly hyperbolic system of conservation laws.

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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