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001040320 005__ 20250428202211.0
001040320 0247_ $$2datacite_doi$$a10.34734/FZJ-2025-01834
001040320 037__ $$aFZJ-2025-01834
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001040320 1001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b0$$eCorresponding author$$ufzj
001040320 1112_ $$aConference on Mathematics of Wave Phenomena$$cKarlsruhe$$d2025-02-24 - 2025-02-28$$wGermany
001040320 245__ $$aNon-scattering wave numbers versus transmission eigenvalues
001040320 260__ $$c2025
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001040320 520__ $$aAn important question arising in inverse problems for wave scattering is whether for a given inhomogeneous bounded obstacle in two dimensions there is an incident wave that does not scatter. Closely connected to this question is the solution of the interior transmission problem.Therefore, let $A$ be the discrete set of non-scattering wave numbers and $B$ be the discrete set of transmission eigenvalues.It is well-known that $A=B\neq \emptyset$ holds for a disk and $B\supsetneq A=\emptyset$ holds for a square. The questions remains whether there is a bounded obstacle for which $A\subsetneq B$ with $A\neq \emptyset$. To address this question, the problem at hand is recasted as a constrained optimization problem using Fourier-Besselfunctions and then finally solved numerically. Some numerical results are presented and interesting observations are made both of which merit further investigation.
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001040320 9141_ $$y2025
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