The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation

M. I. Belishev, I. Lasiecka
2002 E S A I M: Control, Optimisation and Calculus of Variations  
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the "input → state" map in L2-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 ), ut(·, T )} may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the
more » ... pplied to the problem of the boundary data continuation. If T0 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. Mathematics Subject Classification. 93C20, 74B05, 35B65, 34K35. 1 2 , c s := µ ρ 1 2 are the velocities of pressure and shear waves, p -characteristics being ordinary whereas s -characteristics being of multiplicity 2.
doi:10.1051/cocv:2002058 fatcat:7nzakpenozcnbprhosfsdv4isq