scholarly journals The Dirichlet-to-Neumann Map in a Disk with a One-Step Radial Potential: An Analytical and Numerical Study

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 794
Author(s):  
Sagrario Lantarón ◽  
Susana Merchán
Keyword(s):  
Schrödinger Operator ◽  
Numerical Study ◽  
Schrodinger Operator ◽  
Analytical Results ◽  
One Step ◽  
Radial Potential ◽  
Dirichlet To Neumann Map

Herein, we considered the Schrödinger operator with a potential q on a disk and the map that associates to q the corresponding Dirichlet-to-Neumann (DtN) map. We provide some numerical and analytical results on the range of this map and its stability for the particular class of one-step radial potentials.

scholarly journals RECOVERY OF NON-COMPACTLY SUPPORTED COEFFICIENTS OF ELLIPTIC EQUATIONS ON AN INFINITE WAVEGUIDE

2018 ◽  
Vol 19 (5) ◽  
pp. 1573-1600
Author(s):  
Yavar Kian
Keyword(s):  
Schrödinger Operator ◽  
General Class ◽  
Cylindrical Domain ◽  
Schrodinger Operator ◽  
Compactly Supported ◽  
Dirichlet Data ◽  
Unbounded Cylinder ◽  
Boundary Measurements ◽  
Electric Potentials ◽  
Dirichlet To Neumann Map

We consider the unique recovery of a non-compactly supported and non-periodic perturbation of a Schrödinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of a general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different contexts including recovery of some general class of non-compactly supported coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schrödinger operator in a slab.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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