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.

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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017072
Classification : 95B05, 35L60, 35L65
Mots-clés : Linearly degenerate quasilinear hyperbolic systems of conservation laws, local exact boundary controllability, semi-global entropy solutions, ε-approximate front tracking solutions
Li, Tatsien 1 ; Yu, Lei 1

1 
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     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://archive.numdam.org/articles/10.1051/cocv/2017072/}
}
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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://archive.numdam.org/articles/10.1051/cocv/2017072/

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