Well-Posedness Theory for Hyperbolic Systems of Conservation Laws

2001 ◽  
pp. 1-24
Author(s):  
Tai-Ping Liu
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Well Posedness ◽  
Systems Of Conservation Laws

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

High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Elimboto M. Yohana ◽  
Mapundi K. Banda
Keyword(s):  
Optimal Control ◽  
Conservation Laws ◽  
Optimal Control Problems ◽  
Initial Conditions ◽  
Hyperbolic Systems ◽  
Control Problems ◽  
Computational Investigation ◽  
Backward Problem ◽  
Systems Of Conservation Laws ◽  
The Cost

AbstractA computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical flow obtained by optimal initial conditions matches accurately with observations.

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