Identification problems for anisotropic time-fractional subdiffusion equations

Abstract

We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under energy-type overdeterminating conditions. We prove the uniqueness of the solution to the inverse problem when the fractional order $\alpha$ of the derivative is in $(0,1)$. A conditioned existence result is also provided, complemented with a suitable selection of numerical calculations. 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.