Browsing by Author "Rueland, Angkana"

Now showing 1 - 2 of 2

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.
The Calderon problem for the fractional Schrodinger equation with drift
(2020-04-24)
Cekic, Mihajlo
;
Lin, Yi-Hsuan
;
Rueland, Angkana
;
應用數學系
;
Department of Applied Mathematics
We investigate the Calderon problem for the fractional Schrodinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does not enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many generic measurements is discussed. Here the genericity is obtained through singularity theory which might also be interesting in the context of hybrid inverse problems. Combined with the results from Ghosh et al. (Uniqueness and reconstruction for the fractional Calderon problem with a single easurement, 2018. ), this yields a finite measurements constructive reconstruction algorithm for the fractional Calderon problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension n >= 1.