Carleman estimate and an inverse source problem for the Kelvin-Voigt model for viscoelasticity
Analysis of PDEs
2020-01-08 v1
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.
Keywords
Cite
@article{arxiv.1809.06764,
title = {Carleman estimate and an inverse source problem for the Kelvin-Voigt model for viscoelasticity},
author = {O. Y. Imanuvilov and M. Yamamoto},
journal= {arXiv preprint arXiv:1809.06764},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1711.09276