| Issue |
ESAIM: M2AN
Volume 55, Number 1, January-February 2021
|
|
|---|---|---|
| Page(s) | 171 - 207 | |
| DOI | https://doi.org/10.1051/m2an/2020072 | |
| Published online | 18 February 2021 | |
Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order
1
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
2
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
3
Beijing Computational Science Research Center, Beijing 100193, P.R. China
* Corresponding author: buyang.li@polyu.edu.hk, libuyang@gmail.com
Received:
23
April
2020
Accepted:
5
October
2020
We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with a variable fractional order that may depend on the unknown solution. We present a linearly implicit time-stepping method to linearize and discretize the equation in time, and present rigorous analysis for the convergence of numerical solutions based on proved regularity results.
Mathematics Subject Classification: 65M15 / 65M60 / 65M12 / 45K05
Key words: Fractional diffusion equation / variable order / nonlinear / well-posedness / regularity / numerical approximation / convolution quadrature / convergence
© EDP Sciences, SMAI 2021
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