Existence and uniqueness results for a time-fractional nonlinear diffusion equation

In this work we consider a nonlinear ordinary integro-differential equation which arises in the studies of time-fractional porous medium equation. The nonlocality of the resulting free-boundary problem is governed by the Erdélyi–Kober operator which requires using other than classical proof techniqu...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-06, Vol.462 (2), p.1425-1434
Main Authors: Płociniczak, Łukasz, Świtała, Mateusz
Format: Article
Language:English
Subjects:
Erdélyi–Kober operator
Existence and uniqueness
Porous medium
Time-fractional diffusion
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Summary:In this work we consider a nonlinear ordinary integro-differential equation which arises in the studies of time-fractional porous medium equation. The nonlocality of the resulting free-boundary problem is governed by the Erdélyi–Kober operator which requires using other than classical proof techniques. To prove the existence and uniqueness of a compactly supported solution we reduce the free-boundary case to the initial-value problem. Next, we use the sub- and supersolution technique to show that there exists a globally defined unique solution. As a side product, some estimates on the exact solution are found.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.02.050