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@INPROCEEDINGS{Kleefeld:1040320,
      author       = {Kleefeld, Andreas},
      title        = {{N}on-scattering wave numbers versus transmission
                      eigenvalues},
      reportid     = {FZJ-2025-01834},
      year         = {2025},
      abstract     = {An 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.},
      month         = {Feb},
      date          = {2025-02-24},
      organization  = {Conference on Mathematics of Wave
                       Phenomena, Karlsruhe (Germany), 24 Feb
                       2025 - 28 Feb 2025},
      subtyp        = {After Call},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)6},
      doi          = {10.34734/FZJ-2025-01834},
      url          = {https://juser.fz-juelich.de/record/1040320},
}