TY - JOUR
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.
UR - http://hdl.handle.net/10754/667837
UR - http://www.degruyter.com/view/j/fca.2019.22.issue-4/fca-2019-0050/fca-2019-0050.xml
UR - http://www.scopus.com/inward/record.url?scp=85071163612&partnerID=8YFLogxK
U2 - 10.1515/fca-2019-0050
DO - 10.1515/fca-2019-0050
M3 - Article
SN - 1311-0454
VL - 22
SP - 918
EP - 944
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
IS - 4
ER -