Carleman estimate and its application for anomalous slow diffusion equation
Ching-Lung Lin, Gen Nakamura
TL;DR
This paper establishes a Carleman estimate and demonstrates unique continuation for an anomalous diffusion equation with fractional time derivatives, using pseudo-differential operator calculus, advancing understanding of such equations.
Contribution
It introduces a novel Carleman estimate for anomalous diffusion equations with fractional derivatives, enabling unique continuation results.
Findings
Established a Carleman estimate for fractional anomalous diffusion
Proved unique continuation property for solutions
Applied pseudo-differential calculus to derive estimates
Abstract
A Carleman estimate and the unique continuation of solutions for an anomalous diffusion equation with fractional time derivative of order are given. The estimate is derived via some subelliptic estimate for an operator associated to the anomalous diffusion equation using calculus of pseudo-differential operators.
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Taxonomy
TopicsFractional Differential Equations Solutions · Nonlinear Differential Equations Analysis · Differential Equations and Numerical Methods