Parameters Estimation in a Time-Fractiona Parabolic System of Porous Media

Abstract

The simultaneous estimation of coefficients and the initial conditions for model fractional parabolic systems of porous media is reduced to the minimization of a least-squares cost functional. This inverse problem uses information about the pressures at a finite number of space time points. The Frechet gradient of the cost functional is derived. The application of the conjugate gradient method for numerical parameter estimation is also discussed. Computational results with noise-free and noisy data illustrate the efficiency and accuracy of the proposed algorithm.

Keywords

• parabolic system
• time-fractional derivative
• porous media
• parameter estimation
• optimization
• gradient method