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    Regularity theory for time-fractional advection–diffusion–reaction equations

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    Type
    Article
    Authors
    McLean, William cc
    Mustapha, Kassem
    Ali, Raed
    Knio, Omar cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    KAUST Grant Number
    KAUST005
    Date
    2019-08-27
    Online Publication Date
    2019-08-27
    Print Publication Date
    2019-08
    Permanent link to this record
    http://hdl.handle.net/10754/656731
    
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    Abstract
    We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection–diffusion–reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our focus is on proving estimates that are needed for the error analysis of numerical methods. The nonlocal nature of the fractional derivative creates substantial difficulties compared with the case of a classical parabolic PDE. In our analysis, we rely on novel energy methods in combination with a fractional Gronwall inequality and certain properties of fractional integrals.
    Citation
    McLean, W., Mustapha, K., Ali, R., & Knio, O. M. (2020). Regularity theory for time-fractional advection–diffusion–reaction equations. Computers & Mathematics with Applications, 79(4), 947–961. doi:10.1016/j.camwa.2019.08.008
    Sponsors
    The authors thank the University of New South Wales, Australia (Faculty Research Grant “Efficient numerical simulation of anomalous transport phenomena”), the King Fahd University of Petroleum and Minerals, Saudi Arabia (project No. KAUST005) and the King Abdullah University of Science and Technology, Saudi Arabia. ☆ The authors thank the University of New South Wales, Australia (Faculty Research Grant “Efficient numerical simulation of anomalous transport phenomena”), the King Fahd University of Petroleum and Minerals, Saudi Arabia (project No. KAUST005) and the King Abdullah University of Science and Technology, Saudi Arabia.
    Publisher
    Elsevier BV
    Journal
    Computers and Mathematics with Applications
    DOI
    10.1016/j.camwa.2019.08.008
    arXiv
    1902.00850
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0898122119304055
    http://arxiv.org/pdf/1902.00850
    http://arxiv.org/pdf/1902.00850
    http://arxiv.org/pdf/1902.00850
    http://arxiv.org/pdf/1902.00850
    http://arxiv.org/pdf/1902.00850
    http://arxiv.org/pdf/1902.00850
    http://arxiv.org/pdf/1902.00850
    http://arxiv.org/pdf/1902.00850
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.camwa.2019.08.008
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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