Browsing by Author "Lai, Ru-Yu"

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THE CALDERON PROBLEM FOR A SPACE-TIME FRACTIONAL PARABOLIC EQUATION
(2020-01-01)
Lai, Ru-Yu
;
Lin, Yi-Hsuan
;
Rueland, Angkana
;
應用數學系
;
Department of Applied Mathematics
In this article we study an inverse problem for the space-time fractional parabolic operator (partial derivative(t) -Delta)(s) +Q with 0 < s < 1 in any space dimension. We uniquely determine the unknown bounded potential Q from infinitely many exterior Dirichlet-to-Neumann type measurements. This relies on Runge approximation and the dual global weak unique continuation properties of the equation under consideration. In discussing weak unique continuation of our operator, a main feature of our argument relies on a new Carleman estimate for the associated degenerate parabolic Caffarelli- Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.