scholarly journals One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws

2017 ◽  
Vol 107 (1) ◽  
pp. 1-40 ◽  
Author(s):  
Tatsien Li ◽  
Lei Yu
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Null Controllability ◽  
Entropy Solutions ◽  
Exact Boundary ◽  
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.

scholarly journals Dissipative boundary conditions for 2 × 2 hyperbolic systems of conservation laws for entropy solutions in BV

2017 ◽  
Vol 262 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Jean-Michel Coron ◽  
Sylvain Ervedoza ◽  
Shyam Sundar Ghoshal ◽  
Olivier Glass ◽  
Vincent Perrollaz
Keyword(s):  
Boundary Conditions ◽  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Entropy Solutions ◽  
Systems Of Conservation Laws ◽  
Dissipative Boundary
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