Variational Formulation of the Problem of Finding Generalized Solutions for Quasilinear Hyperbolic Systems of Conservation Laws

2021 ◽  
Vol 110 (5-6) ◽  
pp. 972-975
Author(s):  
Yu. G. Rykov
Keyword(s):  
Conservation Laws ◽  
Variational Formulation ◽  
Hyperbolic Systems ◽  
Generalized Solutions ◽  
Quasilinear Hyperbolic Systems ◽  
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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