On the algebraic aspect of singular solutions to conservation laws systems

2006 ◽  
Author(s):  
A. Yu. Khrennikov
Keyword(s):  
Conservation Laws ◽  
Singular Solutions ◽  
Algebraic Aspect

scholarly journals Singular solutions of a fully nonlinear 2 × 2 system of conservation laws

2012 ◽  
Vol 55 (3) ◽  
pp. 711-729 ◽  
Author(s):  
Henrik Kalisch ◽  
Darko Mitrović
Keyword(s):  
Conservation Laws ◽  
Admissible Solution ◽  
Singular Solutions ◽  
Riemann Problems ◽  
Fully Nonlinear ◽  
System Of Conservation Laws ◽  
Image Position ◽  
Complex Valued ◽  
Shock Solution ◽  
Approximation Parameter

AbstractExistence and admissibility of δ-shock solutions is discussed for the non-convex strictly hyperbolic system of equationsThe system is fully nonlinear, i.e. it is nonlinear with respect to both unknowns, and it does not admit the classical Lax-admissible solution for certain Riemann problems. By introducing complex-valued corrections in the framework of the weak asymptotic method, we show that a compressive δ-shock solution resolves such Riemann problems. By letting the approximation parameter tend to zero, the corrections become real valued, and the solutions can be seen to fit into the framework of weak singular solutions defined by Danilov and Shelkovich. Indeed, in this context, we can show that every 2 × 2 system of conservation laws admits δ-shock solutions.

Bosonic Symmetries, Solutions, and Conservation Laws for the Dirac Equation with Nonzero Mass

2013 ◽  
Vol 58 (6) ◽  
pp. 523-533 ◽  
Author(s):  
V.M. Simulik ◽  
◽  
I.Yu. Krivsky ◽  
I.L. Lamer ◽  
◽  
...  
Keyword(s):  
Dirac Equation ◽  
Conservation Laws
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