Regularity theory for time-fractional advection–diffusion–reaction equations
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Grant Number
KAUST005Date
2019-08-27Online Publication Date
2019-08-27Print Publication Date
2019-08Permanent link to this record
http://hdl.handle.net/10754/656731
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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.2019.08.008Sponsors
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 BVarXiv
1902.00850Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0898122119304055http://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