In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem. This methodology is based on an abstract argument for the null controllability of parabolic equations in the presence of source terms and it avoids tackling linearized problems with time dependent coefficients.
Mots-clés : null-controllability, fluid-structure interaction, viscous Burgers equation
@article{COCV_2013__19_1_20_0, author = {Liu, Yuning and Takahashi, Tak\'eo and Tucsnak, Marius}, title = {Single input controllability of a simplified fluid-structure interaction model}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {20--42}, publisher = {EDP-Sciences}, volume = {19}, number = {1}, year = {2013}, doi = {10.1051/cocv/2011196}, mrnumber = {3023058}, zbl = {1270.35259}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2011196/} }
TY - JOUR AU - Liu, Yuning AU - Takahashi, Takéo AU - Tucsnak, Marius TI - Single input controllability of a simplified fluid-structure interaction model JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 20 EP - 42 VL - 19 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2011196/ DO - 10.1051/cocv/2011196 LA - en ID - COCV_2013__19_1_20_0 ER -
%0 Journal Article %A Liu, Yuning %A Takahashi, Takéo %A Tucsnak, Marius %T Single input controllability of a simplified fluid-structure interaction model %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 20-42 %V 19 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2011196/ %R 10.1051/cocv/2011196 %G en %F COCV_2013__19_1_20_0
Liu, Yuning; Takahashi, Takéo; Tucsnak, Marius. Single input controllability of a simplified fluid-structure interaction model. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 1, pp. 20-42. doi : 10.1051/cocv/2011196. http://www.numdam.org/articles/10.1051/cocv/2011196/
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