Well-posedness of time-fractional advection-diffusion-reaction equations

William McLean; Kassem Mustapha; Raed Ali; Omar Knio

doi:10.1515/fca-2019-0050

Well-posedness of time-fractional advection-diffusion-reaction equations

William McLean, Kassem Mustapha, Raed Ali, Omar Knio

Department of Mathematics

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

44 Scopus citations

Abstract

We establish the well-posedness of an initial-boundary value problem for a general class of linear time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our analysis relies on novel energy methods in combination with a fractional Gronwall inequality and properties of fractional integrals.

Original language	English
Pages (from-to)	918-944
Number of pages	27
Journal	Fractional Calculus and Applied Analysis
Volume	22
Issue number	4
DOIs	https://doi.org/10.1515/fca-2019-0050
State	Published - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019 Diogenes Co., Sofia

Keywords

Fractional Gronwall inequality
Fractional PDE
Galerkin method
Volterra integral equation
Weak solution

ASJC Scopus subject areas

Analysis
Applied Mathematics

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Cite this

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abstract = "We establish the well-posedness of an initial-boundary value problem for a general class of linear time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our analysis relies on novel energy methods in combination with a fractional Gronwall inequality and properties of fractional integrals.",

keywords = "Fractional Gronwall inequality, Fractional PDE, Galerkin method, Volterra integral equation, Weak solution",

author = "William McLean and Kassem Mustapha and Raed Ali and Omar Knio",

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AU - McLean, William

AU - Mustapha, Kassem

AU - Ali, Raed

AU - Knio, Omar

PY - 2019/8/1

Y1 - 2019/8/1

N2 - We establish the well-posedness of an initial-boundary value problem for a general class of linear time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our analysis relies on novel energy methods in combination with a fractional Gronwall inequality and properties of fractional integrals.

AB - We establish the well-posedness of an initial-boundary value problem for a general class of linear time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our analysis relies on novel energy methods in combination with a fractional Gronwall inequality and properties of fractional integrals.

KW - Fractional Gronwall inequality

KW - Fractional PDE

KW - Galerkin method

KW - Volterra integral equation

KW - Weak solution

UR - https://www.scopus.com/pages/publications/85071163612

U2 - 10.1515/fca-2019-0050

DO - 10.1515/fca-2019-0050

M3 - Article

AN - SCOPUS:85071163612

SN - 1311-0454

VL - 22

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JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 4

ER -

Well-posedness of time-fractional advection-diffusion-reaction equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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