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

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

36 Scopus citations

Abstract

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 (US)
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 - Aug 27 2019

Bibliographical note

KAUST Repository Item: Exported on 2021-12-15
Acknowledged KAUST grant number(s): KAUST005
Acknowledgements: The authors thank the University of New South Wales (Faculty Research Grant “Efficient numerical simulation of anomalous transport phenomena”), the King Fahd University of Petroleum and Minerals (project No. KAUST005) and the King Abdullah University of Science and Technology.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "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.",

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T1 - Well-posedness of time-fractional advection-diffusion-reaction equations

AU - McLean, William

AU - Mustapha, Kassem

AU - Ali, Raed

AU - Knio, Omar

N1 - KAUST Repository Item: Exported on 2021-12-15 Acknowledged KAUST grant number(s): KAUST005 Acknowledgements: The authors thank the University of New South Wales (Faculty Research Grant “Efficient numerical simulation of anomalous transport phenomena”), the King Fahd University of Petroleum and Minerals (project No. KAUST005) and the King Abdullah University of Science and Technology.

PY - 2019/8/27

Y1 - 2019/8/27

N2 - 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.

AB - 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.

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M3 - Article

SN - 1311-0454

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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

ASJC Scopus subject areas

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