Backward Uniqueness for Thermoelastic Plates with Rotational Forces

Abstract

This paper provides a backward uniqueness theorem for thermoelastic plate models which account for rotational forces, under all sets of canonical boundary conditions, including the most challenging case of so-called free boundary conditions. The proof is abstract and accomodates space variable coefficients in the model. This result is derived in two steps. First, in Section 3, a new backward uniqueness theorem for strongly continuous semigroups is given, which is of interest in itself. It is based on the assumption that the resolvent operator of the generator be bounded on suitable rays of the complex plane. Its proof uses the Phragmen-Lindelof Theorem. Next, the paper verifies a fortiori the required resolvent conditions, under all sets of canonical boundary conditions. The explicit proof (in Section 4) considers the most demanding case of free boundary conditions. An abstract version of this proof, and a corresponding backward uniqueness result, are then noted in Section 5, which gives the most general result of this paper. It covers thermoelastic wave equations as well.