Local logarithmic stability of an inverse coefficient problem for a singular heat equation with an inverse-square potential

Abstract

An inverse problem of the determination of the coefficient in the equation: is considered. The main difficulty here as compared with the existing result is that there is a singular potential in the equation. A local logarithmic stability estimate is obtained using the method of Carleman estimates. Our proof relies on the Bukhgeim–Klibanov method which was originated in [Bukhgeim AL, Klibanov MV. Uniqueness in the large of a class of multidiimensional inverse problems. Dokl Akad Nauk SSSR. 1981;17:244–247] to prove inverse source or coefficient results.