scholarly journals Lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small BV initial data: Shocks and contact discontinuities

2012 ◽  
Vol 387 (2) ◽  
pp. 698-720 ◽  
Author(s):  
Zhi-Qiang Shao
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Discontinuous Solutions ◽  
Quasilinear Hyperbolic Systems ◽  
Contact Discontinuities ◽  
Systems Of Conservation Laws

Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws

2018 ◽  
Vol 24 (2) ◽  
pp. 793-810
Author(s):  
Tatsien Li ◽  
Lei Yu
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Front Tracking ◽  
Entropy Solutions ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Quasilinear Hyperbolic Systems ◽  
Exact Boundary ◽  
Systems Of Conservation Laws ◽  
Linearly Degenerate

In this paper, we study the local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws with characteristics of constant multiplicity. We prove the two-sided boundary controllability, the one-sided boundary controllability and the two-sided boundary controllability with fewer controls, by applying the strategy used in [T. Li and L. Yu, J. Math. Pures et Appl. 107 (2017) 1–40; L. Yu, Chinese Ann. Math., Ser. B (To appear)]. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions, and on some further properties of both ε-approximate front tracking solutions and limit solutions.

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