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001048792 1001_ $$00000-0002-9648-6476$$aHarris, Isaac$$b0$$eCorresponding author
001048792 245__ $$aExistence of transmission eigenvalues for biharmonic scattering by a clamped planar region
001048792 260__ $$aBristol [u.a.]$$bInst.$$c2025
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001048792 520__ $$aIn this paper, we study the so-called clamped transmission eigenvalue problem. This is a new transmission eigenvalue problem that is derived from the scattering of an impenetrable clamped obstacle in a thin elastic plate. The scattering problem is modeled by a biharmonic wave operator given by the Kirchhoff-Love infinite plate problem in the frequency domain. These scattering problems have not been studied to the extent of other models. Unlike other transmission eigenvalue problems, the problem studied here is a system of homogeneous PDEs defined in all of $\mathbb{R}^2$ . This provides unique analytical and computational difficulties when studying the clamped transmission eigenvalue problem. We are able to prove that there exist infinitely many real clamped transmission eigenvalues. This is done by studying the equivalent variational formulation. We also investigate the relationship of the clamped transmission eigenvalues to the Dirichlet and Neumann eigenvalues of the negative Laplacian for the bounded scattering obstacle.
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001048792 7001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b1
001048792 7001_ $$00000-0001-9924-4133$$aLee, Heejin$$b2
001048792 773__ $$0PERI:(DE-600)1477292-9$$a10.1088/1361-6420/ae259b$$n12$$p125002$$tInverse problems$$v41$$x0266-5611$$y2025
001048792 8564_ $$uhttps://juser.fz-juelich.de/record/1048792/files/Harris_2025_Inverse_Problems_41_125002.pdf$$yOpenAccess
001048792 8564_ $$uhttps://juser.fz-juelich.de/record/1048792/files/TE-Existence2.pdf$$yOpenAccess
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