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

Buyang Li; Hong Wang; Jilu Wang

doi:10.1051/m2an/2020072

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

Buyang Li, Hong Wang, Jilu Wang

Research output: Journal article publication › Journal article › Academic research › peer-review

12 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	171-207
Number of pages	37
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	55
Issue number	1
DOIs	https://doi.org/10.1051/m2an/2020072
Publication status	Published - 1 Jan 2021

Keywords

Convergence
Convolution quadrature
Fractional diffusion equation
Nonlinear
Numerical approximation
Regularity
Variable order
Well-posedness

ASJC Scopus subject areas

Analysis
Numerical Analysis
Modelling and Simulation
Computational Mathematics
Applied Mathematics

More information

10.1051/m2an/2020072

http://hdl.handle.net/10397/93882

Cite this

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AU - Wang, Hong

AU - Wang, Jilu

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Y1 - 2021/1/1

N2 - 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.

AB - 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.

KW - Convergence

KW - Convolution quadrature

KW - Fractional diffusion equation

KW - Nonlinear

KW - Numerical approximation

KW - Regularity

KW - Variable order

KW - Well-posedness

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U2 - 10.1051/m2an/2020072

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M3 - Journal article

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SP - 171

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JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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