Well-posedness of time-fractional advection-diffusion-reaction equations
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Grant NumberKAUST005
Permanent link to this recordhttp://hdl.handle.net/10754/667837
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AbstractAbstract 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.
CitationMcLean, W., Mustapha, K., Ali, R., & Knio, O. (2019). Well-posedness of time-fractional advection-diffusion-reaction equations. Fractional Calculus and Applied Analysis, 22(4), 918–944. doi:10.1515/fca-2019-0050
SponsorsThe 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.
PublisherWalter de Gruyter GmbH