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

Abstract

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.