Numerical reconstructions of a source term in a mobile-immobile diffusion model from the partial interior observation
Abstract
Abstract We consider an inverse source problem in the two-time-scale mobile-immobile fractional diffusion model from partial interior observation. Theoretically, we combine the fractional Duhamel’s principle with the weak vanishing property to establish the uniqueness of this inverse problem. Numerically, we adopt an optimal control approach for determining the source term. A coupled forward-backward system of equations is derived using the first-order optimality condition. Finally, we construct a finite element conjugate gradient algorithm for the numerical inversion of the source term. Several experiments are presented to show the utility of the method.
Fields of Study & Subjects
Numerical methods in inverse problems
Fractional Differential Equations Solutions
Microwave Imaging and Scattering Analysis
Publication details
- Journal / source
- Journal of Inverse and Ill-Posed Problems
- Publisher
- Walter de Gruyter GmbH
- Volume
- 34
- Issue
- 2
- Pages
- 241–254
- Publication date
- 20 February 2026
- Language
- EN