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.
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DOI : 10.1051/cocv/2019050
Mots-clés : Quasilinear hyperbolic system, exact boundary controllability of nodal profile, classical solutions, asymptotic stability
@article{COCV_2020__26_1_A67_0,
author = {Wang, Libin and Wang, Ke},
title = {Asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019050},
mrnumber = {4151426},
zbl = {1450.35070},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019050/}
}
TY - JOUR AU - Wang, Libin AU - Wang, Ke TI - Asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019050/ DO - 10.1051/cocv/2019050 LA - en ID - COCV_2020__26_1_A67_0 ER -
%0 Journal Article %A Wang, Libin %A Wang, Ke %T Asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019050/ %R 10.1051/cocv/2019050 %G en %F COCV_2020__26_1_A67_0
Wang, Libin; Wang, Ke. Asymptotic stability of the exact boundary controllability of nodal profile for quasilinear hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 67. doi : 10.1051/cocv/2019050. http://www.numdam.org/articles/10.1051/cocv/2019050/
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Supported by the National Natural Science Foundation of China (Nos. 11831011, 11771091, 11601074 and 11671075).
