1 results
The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation
-
- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 8 / 2002
- Published online by Cambridge University Press:
- 15 August 2002, pp. 143-167
- Print publication:
- 2002
-
- Article
- Export citation
-
The boundary control problem for the dynamical Lame system(isotropic elasticity model) is considered. The continuity ofthe “input → state" map in L 2-norms is established. A structure of thereachable sets for arbitrary T>0 is studied.In general case, only the first component $u(\cdot ,T)$
of thecomplete state $\{ u(\cdot ,T),u_t(\cdot ,T)\}$ 
may be controlled, an approximate controllability occurring inthe subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundarydata continuation. If T 0 exceeds the time neededfor shear waves to fill the entire domain, then the responseoperator (“input → output" map) $R^{2T_0}$ 
uniquely determinesRT for any T>0. A procedure recovering R ∞via $R^{2T_0}$ is also described.
