On Stability of the Solution of Multidimensional Inverse Problem for the Schrödinger Equation

¹ Kazakh National Pedagogical University named after Abai, Almaty, Kazakhstan
² International Kazakh-Turkish University named after Khoja Ahmed Yasavi, Turkestan, Kazakhstan

^* Corresponding author. E-mail: berdyshev@mail.ru, murat.sultanov@ayu.edu.kz

Abstract

In the paper we prove the theorems of conditional stability of the solution of the inverse problem of determining the potential a(x) of the Schrödinger equation iu_t + Δ_u + a(x)u = 0, in the multidimensional case x ∈ Rⁿ, in non-stationary and spectral formulations. The method of proof in the non-stationary formulation is based on the Carleman type a priori weight estimates with operator coefficients. The stability of the solution of the inverse problem in the spectral formulation is investigated using the connection of this formulation with the corresponding formulation of the inverse dynamic problem.