Global structure stability of Riemann solutions for linearly degenerate hyperbolic conservation laws under small BV perturbations of the initial data

2010 ◽  
Vol 11 (5) ◽  
pp. 3791-3808 ◽  
Author(s):  
Zhi-Qiang Shao
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Global Structure ◽  
Structure Stability ◽  
Riemann Solutions ◽  
Hyperbolic Conservation ◽  
Linearly Degenerate

scholarly journals A NOTE ON THE NEW GLIMM FUNCTIONAL FOR GENERAL SYSTEMS OF HYPERBOLIC CONSERVATION LAWS

2010 ◽  
Vol 20 (05) ◽  
pp. 815-842 ◽  
Author(s):  
JIALE HUA ◽  
TONG YANG
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Conservation ◽  
Glimm Scheme ◽  
Codimension One ◽  
General Systems ◽  
Whole Space ◽  
Hyperbolicity Assumption ◽  
Linearly Degenerate ◽  
Characteristic Field

For systems of hyperbolic conservation laws, a new Glimm functional was recently constructed when the linearly degenerate manifold in each characteristic field is either the whole space or it consists of a finitely many smooth and transversal manifolds of codimension one. This new functional leads to the neat consistency and convergence rate estimation of the Glimm scheme. In this paper, by the motivation of the result in Ref. 2, we show that the corresponding new Glimm functional can be constructed for general systems only under the strict hyperbolicity assumption.

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