Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order

被引：0
|
作者：
Li, Buyang [1 ]
Wang, Hong [2 ]
Wang, Jilu [3 ]
机构：
[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, United States
[3] Beijing Computational Science Research Center, Beijing,100193, China
来源：
ESAIM: Mathematical Modelling and Numerical Analysis | 2021年 / 55卷 / 01期
关键词：
Diffusion - Partial differential equations - Nonlinear equations - Convergence of numerical methods - Porous materials;
D O I：
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中图分类号：
学科分类号：
摘要：
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. © EDP Sciences, SMAI 2021.
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页码：171 / 207
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