Determination of the absorption coefficient from discrete data

Subject of research: inverse problems concerning the determination of an absorption coefficient in a parabolic equation from discrete (pointwise) data. Purpose of research: establishing the well-posedness of the problem of determining the lower-order coefficient in a parabolic equation from pointwise overdetermination conditions; proving the existence and uniqueness of a solution in Sobolev spaces. Research methods: a priori estimates, Schauder’s fixed-point theorem, and the theory of parabolic operators. Objects of research: parabolic equations with an unknown absorption coefficient represented as a linear combination of known functions with unknown coefficients. Research findings: a theorem on the existence and uniqueness of solutions in Sobolev spaces is proven, and a priori estimates are derived. The method is constructive and can serve as a foundation for developing a numerical algorithm for the approximate solution of the inverse problem.