We study the Helmholtz equation in the exterior of an infinite perturbed cylinder with a Dirichlet boundary condition. Existence and uniqueness of solutions are established using the variational technique introduced ( SIAM J. Math. Anal. 2005; 37 (2):598–618). We also provide stability estimates with explicit dependence of the constants in terms of the frequency and the perturbed cylinder thickness.
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Claeys et al. (2006) studied this question.
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