Maps of Convex Sets and Invariant Regions¶for Finite-Difference Systems¶of Conservation Laws

2001 ◽  
Vol 160 (3) ◽  
pp. 245-269 ◽  
Author(s):  
Hermano Frid
Keyword(s):  
Finite Difference ◽  
Conservation Laws ◽  
Convex Sets ◽  
Difference Systems ◽  
Systems Of Conservation Laws ◽  
Invariant Regions

scholarly journals Extensions of Noether's Second Theorem: from continuous to discrete systems

2011 ◽  
Vol 467 (2135) ◽  
pp. 3206-3221 ◽  
Author(s):  
Peter E. Hydon ◽  
Elizabeth L. Mansfield
Keyword(s):  
Finite Difference ◽  
Conservation Laws ◽  
Variational Problem ◽  
Discrete Systems ◽  
Lagrange Equations ◽  
Difference Systems

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler–Lagrange equations of any variational problem whose symmetries depend on a set of free or partly constrained functions. Our approach extends further to deal with finite-difference systems. The results are easy to apply; several well-known continuous and discrete systems are used as illustrations.

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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