Recovery of a potential in a fractional diffusion equation

Abstract

We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse Sturm-Liouville problem and these are sufficient to apply standard uniqueness results for this case. We also look at reconstruction methods and in particular examine the issue of stability of the solution with respect to the data. The outcome shows the inverse problem to be severely ill-conditioned and we consider the differences between the cases of fractional and of classical diffusion.

arXiv comment11 pages journal submission

References in corpus (1)

• Recovering an Unknown Source in a Fractional Diffusion Problem

Cited by in corpus (3)

• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations
• Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions