TY - JOUR
T1 - Regularity theory for time-fractional advection–diffusion–reaction equations
AU - McLean, William
AU - Mustapha, Kassem
AU - Ali, Raed
AU - Knio, Omar
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KAUST005
Acknowledgements: 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.
PY - 2019/8/27
Y1 - 2019/8/27
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/656731
UR - https://linkinghub.elsevier.com/retrieve/pii/S0898122119304055
UR - http://www.scopus.com/inward/record.url?scp=85071188416&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2019.08.008
DO - 10.1016/j.camwa.2019.08.008
M3 - Article
SN - 0898-1221
VL - 79
SP - 947
EP - 961
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 4
ER -