Identification problems for anisotropic time-fractional subdiffusion equations

Abstract We investigate the inverse problem consisting in the identification of constant coefficients appearing in a finite sum of positive self-adjoint operators governing a fractional-in-time partial differential equation on a Hilbert space under overdeterminating conditions. We prove the uniqueness of the solution to the inverse problem when the fractional order $\alpha$ of the derivative is in $(0,1)$. Also a conditioned existence result is provided. A suitable selection of numerical calculations complements the existence result by giving a visual description of the shape of some key sets related to our problem in special cases in dimension two. In addition, we prove that, as $\alpha\to 1^{-}$, the solution corresponding to $\alpha$ tends to the classical one ($\alpha=1$). Applications to examples of heat diffusion and elasticity are presented.