Volume 55, Number 1, January-February 2021
|Page(s)||171 - 207|
|Published online||18 February 2021|
Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order
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
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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