Global existence and strong trace property of entropy solutions by the source-concentration Glimm scheme for nonlinear hyperbolic balance laws

2019 ◽  
Vol 26 (4) ◽  
pp. 371-394
Author(s):  
Shih-Wei Chou ◽  
John M. Hong ◽  
Ying-Chieh Lin
Keyword(s):  
Global Existence ◽  
Entropy Solutions ◽  
Balance Laws ◽  
Glimm Scheme ◽  
Hyperbolic Balance Laws ◽  
Trace Property ◽  
Source Concentration

scholarly journals A remark on the Glimm scheme for inhomogeneous hyperbolic systems of balance laws

2015 ◽  
Vol 12 (04) ◽  
pp. 787-797 ◽  
Author(s):  
Cleopatra Christoforou
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Weak Solutions ◽  
State Vector ◽  
Equilibrium Solution ◽  
Hyperbolic Systems ◽  
Balance Laws ◽  
Glimm Scheme ◽  
Systems Of Balance Laws ◽  
The Cauchy Problem

General hyperbolic systems of balance laws with inhomogeneous flux and source are studied. Global existence of entropy weak solutions to the Cauchy problem is established for small BV data under appropriate assumptions on the decay of the flux and the source with respect to space and time. There is neither a hypothesis about equilibrium solution nor about the dependence of the source on the state vector as previous results have assumed.

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