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.
Keywords: Fractional diffusion equation, variable order, nonlinear, well-posedness, regularity, numerical approximation, convolution quadrature, convergence
@article{M2AN_2021__55_1_171_0,
author = {Li, Buyang and Wang, Hong and Wang, Jilu},
title = {Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {171--207},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {1},
doi = {10.1051/m2an/2020072},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020072/}
}
TY - JOUR AU - Li, Buyang AU - Wang, Hong AU - Wang, Jilu TI - Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 171 EP - 207 VL - 55 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020072/ DO - 10.1051/m2an/2020072 LA - en ID - M2AN_2021__55_1_171_0 ER -
%0 Journal Article %A Li, Buyang %A Wang, Hong %A Wang, Jilu %T Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 171-207 %V 55 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020072/ %R 10.1051/m2an/2020072 %G en %F M2AN_2021__55_1_171_0
Li, Buyang; Wang, Hong; Wang, Jilu. Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 1, pp. 171-207. doi: 10.1051/m2an/2020072
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