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 the 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. Finally as a related system, we consider an isothermal compressible fluid system and apply the Carleman estimate to establish the Lipschitz stability for an inverse source problem for the compressible fluid system.

arXiv admin note: text overlap with arXiv:1711.09276

References in corpus (4)

• Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations
• Carleman estimate and application to an inverse source problem for a viscoelasticity model in anisotropic case
• Carleman estimate and an inverse source problem for the Kelvin-Voigt model for viscoelasticity
• Carleman estimate for linear viscoelasticity equations and an inverse source problem

Cited by in corpus (3)

• On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements
• A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids
• Carleman estimate and an inverse source problem for the Kelvin-Voigt model for viscoelasticity