Remarks on energy approach for global existence of some one-dimension quasilinear hyperbolic systems

2019 ◽  
Vol 267 (11) ◽  
pp. 6125-6132 ◽  
Author(s):  
Dongbing Zha
Keyword(s):  
Global Existence ◽  
Hyperbolic Systems ◽  
Energy Approach ◽  
One Dimension ◽  
Quasilinear Hyperbolic Systems

GLOBAL EXISTENCE OF PIECEWISE C1 SOLUTIONS TO THE GENERALIZED RIEMANN PROBLEM

2004 ◽  
Vol 01 (02) ◽  
pp. 329-350 ◽  
Author(s):  
TATSIEN LI ◽  
LIBIN WANG
Keyword(s):  
Global Existence ◽  
Riemann Problem ◽  
Hyperbolic Systems ◽  
Quasilinear Hyperbolic Systems ◽  
Generalized Riemann Problem ◽  
Contact Discontinuities ◽  
Systems Of Conservation Laws ◽  
Global Existence And Uniqueness ◽  
Linearly Degenerate ◽  
Characteristic Field

Assuming that each characteristic field is either genuinely nonlinear or linearly degenerate in the sense of Lax, we prove the global existence and uniqueness of piecewise C1 solution containing n small amplitude waves (shocks corresponding to genuinely nonlinear fields and contact discontinuities corresponding to linearly degenerate fields) for the generalized Riemann problem associated with quasilinear hyperbolic systems of conservation laws with small, decaying, piecewise C1 initial data. The solution possesses a global structure similar to that of the similarity solution to the corresponding Riemann problem.

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