An optimal filtering method for a time-fractional inverse advection-dispersion problem
-
Jingjun Zhao
and
Songshu Liu
Abstract
We consider an inverse problem for a time-fractional advection-dispersion equation, where the measured data is given at x = 1 and the solution is sought in the interval 0 ≤ x < 1. Such a problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α ∈ (0,1). We show that the inverse problem for a time-fractional advection-dispersion equation is severely ill-posed and we further apply an optimal filtering regularization method to solve it, based on the solution in the frequency domain. The corresponding convergence estimates are provided. To illustrate the results, an example is constructed to show the feasibility and efficiency of the proposed method.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11101109
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11271102
Funding source: Natural Science Foundation of Hei-long-jiang Province of China
Award Identifier / Grant number: A201107
The authors wish to thank the referees for their valuable comments.
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Preface
- Lq-regularization for the inverse Robin problem
- Hybrid Newton-type methods for reconstructing sound-soft obstacles from a single far field
- Numerical simulation and parameters inversion for non-symmetric two-sided fractional advection-dispersion equations
- A coupled model of partial differential equations for uranium ores heap leaching and its parameters identification
- An optimal filtering method for a time-fractional inverse advection-dispersion problem
- Simultaneous determination of thickness, thermal conductivity and porosity in textile material design
- Nuclear norm and indicator function model for matrix completion
- Calibrating the model parameters in pricing using the trust region method
- An adaptive multigrid conjugate gradient method for permeability identification of nonlinear diffusion equation
- Reconstruction of prograde and retrograde Chandler excitation
