The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation
ESAIM: Control, Optimisation and Calculus of Variations, Volume 8  (2002), p. 143-167

The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input state” map in L 2 -norms is established. A structure of the reachable sets for arbitrary T>0 is studied. In general case, only the first component u(·,T) of the complete state {u(·,T),u t (·,T)} may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation. If T 0 exceeds the time needed for shear waves to fill the entire domain, then the response operator (“input output” map) R 2T 0 uniquely determines R T for any T>0. A procedure recovering R via R 2T 0 is also described.

DOI : https://doi.org/10.1051/cocv:2002058
Classification:  93C20,  74B05,  35B65,  34K35
Keywords: isotropic elasticity, dynamical Lame system, regularity of solutions, structure of sets reachable from the boundary in a short time, boundary controllability
@article{COCV_2002__8__143_0,
     author = {Belishev, M. I. and Lasiecka, Irena},
     title = {The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     pages = {143-167},
     doi = {10.1051/cocv:2002058},
     zbl = {1064.93019},
     mrnumber = {1932948},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__8__143_0}
}
Belishev, M. I.; Lasiecka, I. The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002) , pp. 143-167. doi : 10.1051/cocv:2002058. http://www.numdam.org/item/COCV_2002__8__143_0/

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