Carleman estimate and an inverse source problem for the Kelvin?Voigt model for viscoelasticity

We consider the Kelvin?Voigt model for the viscoelasticity, and prove a Carleman estimate for functions without compact supports. Then we apply this Carleman estimate to prove the Lipschitz stability in determining a spatial varying function in an external source term of Kelvin?Voigt model by a single measurement.