On the uniqueness of the continuation for a thermoelasticity system

We obtain new uniqueness of the continuation results for the thermoelasticity system on the plane. The crucial ingredient of the proofs is the use of Carleman-type estimates with two large parameters for basic second order partial differential operators with constant coefficients. We derive these estimates by applying differential quadratic forms. The proposed technique can be of value when studying similar questions for systems of partial differential equations of upper triangular principal structure. The results can be applied to control theory and inverse problems.