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.
Accepté le :
DOI : 10.1051/cocv/2017072
Mots clés : Linearly degenerate quasilinear hyperbolic systems of conservation laws, local exact boundary controllability, semi-global entropy solutions, ε-approximate front tracking solutions
@article{COCV_2018__24_2_793_0,
author = {Li, Tatsien and Yu, Lei},
title = {Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws\protect\textsuperscript{,}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {793--810},
publisher = {EDP-Sciences},
volume = {24},
number = {2},
year = {2018},
doi = {10.1051/cocv/2017072},
zbl = {1403.93042},
mrnumber = {3816415},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2017072/}
}
TY - JOUR AU - Li, Tatsien AU - Yu, Lei TI - Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws, JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 793 EP - 810 VL - 24 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2017072/ DO - 10.1051/cocv/2017072 LA - en ID - COCV_2018__24_2_793_0 ER -
%0 Journal Article %A Li, Tatsien %A Yu, Lei %T Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws, %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 793-810 %V 24 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2017072/ %R 10.1051/cocv/2017072 %G en %F COCV_2018__24_2_793_0
Li, Tatsien; Yu, Lei. Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws,. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 793-810. doi : 10.1051/cocv/2017072. http://www.numdam.org/articles/10.1051/cocv/2017072/
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