The dynamical Lame system: Regularity of solutions, boundary controllability and 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. If To exceeds the time needed for shear waves to fill the entire domain, then the response operator ("input → output" map) R 2T0 uniquely determines RT for any T > 0. A procedure recovering R∞ via R2T0 is also described. © EDP Sciences, SMAI 2002.

Publication Title

ESAIM - Control, Optimisation and Calculus of Variations