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Communications in Partial Differential Equations Volume 41, 2016 - Issue 5
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Original Articles

Unique continuation property for anomalous slow diffusion equation

Ching-Lung LinDepartment of Mathematics and Research Center for Theoretical Sciences, NCTS, National Cheng-Kung University, Tainan, Taiwan
&
Gen NakamuraDepartment of Mathematics, Inha University, Incheon, South Korea;Department of Mathematics, Hokkaido University, Sapporo, JapanCorrespondence[email protected]
Pages 749-758 | Received 02 Apr 2014, Accepted 12 Dec 2015, Published online: 25 Apr 2016
 
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ABSTRACT

A Carleman estimate and the unique continuation of solutions for an anomalous diffusion equation with fractional time derivative of order 0 < α <1 are given. The estimate is derived through some subelliptic estimates for an operator associated to the anomalous diffusion equation using calculus of pseudo-differential operators.

MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgment

We thank the referee for valuable comments to improve the paper.

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