Unique continuation for over-determined Kirchoff plate equations and related thermoelastic systems


We present unique continuation results for two over-determined problems: one involving a Kirchoff plate equation and one involving a related thermoelastic system, both with variable coefficient transmission coefficient and zero Cauchy data on an arbitrarily small portion of the boundary. Besides being of interest in themselves, both these two unique continuation results are critically invoked in the solution of a controllability problem (exact in the mechanical variables {w, wt} and, simultaneously, approximate in the thermal variable θ) of thermoelastic plates, by means of boundary controls, either in the hinged/Dirichlet boundary conditions, or else in the clamped/Dirichlet boundary conditions [E-L-T.1]-[E-L-T.3].

Publication Title

Journal of Inverse and Ill-Posed Problems