Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation
Abstract
Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues. In this paper, we prove the uniqueness of determining the variable fractional order of the homogeneous Dirichlet boundary-value problem of the one-sided linear variable-order space-fractional diffusion equation with some observed values of the unknown solutions near the boundary of the spatial domain. We base on the analysis to develop a spectral-Galerkin Levenberg–Marquardt method and a finite difference Levenberg–Marquardt method to numerically invert the variable order. We carry out numerical experiments to investigate the numerical performance of these methods.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 10, 2020
- Source ID
- 10.1515/jiip-2019-0040
Entities
People
- Hong Wang
- Jin Cheng
- Xiangcheng Zheng
- Yiqun Li
Organizations
- Army Research Office
- Fudan University
- National Natural Science Foundation of China
- National Science Foundation
- University of South Carolina