Asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems

2020 ◽  
Vol 26 ◽  
pp. 67 ◽  
Author(s):  
Libin Wang ◽  
Ke Wang
Keyword(s):  
Asymptotic Stability ◽  
Control Function ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Boundary Function ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Quasilinear Hyperbolic Systems ◽  
Exact Boundary

In this paper, we consider the asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems. We will prove that if the nodal profile and the given boundary function possess an exponential or polynomial decaying property, then the boundary control function and the solution to the corresponding mixed initial-boundary value problem will possess the same decaying property.

Local Exact Boundary Controllability for Nonlinear Vibrating String Equations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4062-4071 ◽  
Author(s):  
Ta-Tsien Li ◽  
Yu-Lan Xu
Keyword(s):  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Quasilinear Hyperbolic Systems ◽  
Exact Boundary ◽  
Vibrating String ◽  
Initial Boundary Value ◽  
String Problems

Based on the theory of semiglobal C1 solutions to a class of nonlocal mixed initial-boundary value problems for quasilinear hyperbolic systems, we establish the local exact boundary controllability for a class of nonlinear vibrating string problems with boundary condition of the third type on one end.

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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