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

^*Corresponding author for this work

Hong Kong Polytechnic University
University of South Carolina
China Academy of Engineering Physics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

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

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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.",

keywords = "Convergence, Convolution quadrature, Fractional diffusion equation, Nonlinear, Numerical approximation, Regularity, Variable order, Well-posedness",

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AU - Li, Buyang

AU - Wang, Hong

AU - Wang, Jilu

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PY - 2021/1/1

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

UR - https://www.scopus.com/pages/publications/85101196693

U2 - 10.1051/m2an/2020072

DO - 10.1051/m2an/2020072

M3 - 文章

AN - SCOPUS:85101196693

SN - 2822-7840

VL - 55

SP - 171

EP - 207

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

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