Volume 8, 2002A tribute to JL Lions
|Page(s)||143 - 167|
|Published online||15 August 2002|
The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation
Saint-Petersburg Department of
the Steklov Mathematical Institute (POMI), Fontanka 27,
St. Petersburg 191011, Russia; firstname.lastname@example.org.
2 Department of Mathematics, University of Virginia, Charlottesville, VA 22901, USA; email@example.com.
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 of the complete state 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 T0 exceeds the time needed for shear waves to fill the entire domain, then the response operator (“input → output" map) uniquely determines RT for any T>0. A procedure recovering R∞ via is also described.
Mathematics Subject Classification: 93C20 / 74B05 / 35B65 / 34K35
Key words: Isotropic elasticity / dynamical Lame system / regularity of solutions / structure of sets reachable from the boundary in a short time / boundary controllability.
© EDP Sciences, SMAI, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.