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Title: On uniqueness in some physical systems
Author: Symons, Frederick
ISNI:       0000 0004 6350 9154
Awarding Body: Cardiff University
Current Institution: Cardiff University
Date of Award: 2017
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In this work we present some uniqueness and cloaking results for a related pair of inverse problems. The first concerns recovering the parameter q in a Bessel-type operator pencil, over L^2(0, 1; rdr) from (a generalisation of) the Weyl–-Titchmarsh boundary m-function. We assume that both coefficients, w and q, are singular at 0. We prove q is uniquely determined by the sequence m(-n^2) (n = 1, 2, 3, ...), using asymptotic and spectral analysis and m-function interpolation results. For corollary we find, in a halfdisc with a singular “Dirichlet-point” boundary condition on the straight edge, a singular radial Schroedinger potential is uniquely determined by Dirichlet-to- Neumann boundary measurements on the semi-circular edge. The second result concerns recovery of three things—a Schroedinger potential in a planar domain, a Dirichlet-point boundary condition on part of the boundary, and a self-adjointness-imposing condition—from Dirichlet-to-Neumann measurements on the remaining boundary. With modern approaches to the inverse conductivity problem and a solution-space density argument we show the boundary condition cloaks the potential and vice versa. Appealing to negative eigen-value asymptotics we find the full-frequency problem has full uniqueness.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics