The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input $\to$ 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....

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 $\{u(·,T),u_t(·,T)\}$ 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....