Fractional Diffusion Equation Inverse Problem Boundary Spectral Data Eigenfunction Expansion
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 14, No 1, (2011), 31p-55p
We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.