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Abstract
We study the resonances (or sattering frequenaes) associated with the syutem of elastic wave equations in an unbounded region Ω which is the union of a (bounded) cavity C, an (unbounded) exterior E and a thin channel Z conneding C with E. We show that as the channel gets narrower there are resonances of Ω which converge to the eigenvalues of the (vector) operator in the cavity C
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1Pontificia Universidad CaMlica de Chile. Fscultad de Matemdticas. Cssilla 306, Corma, Santiago, Chile.
2National Laboratory of Scientific Computation, LNCCfCNPq. Rua Getulio Vargas 333,Quitandinha, Petropolis, RJ CEP 26651470, Brad and Institute of Mathematics UFRJ, P.O.Box 68530, Rio de Janeiro, RJ Brasil.
1Pontificia Universidad CaMlica de Chile. Fscultad de Matemdticas. Cssilla 306, Corma, Santiago, Chile.
2National Laboratory of Scientific Computation, LNCCfCNPq. Rua Getulio Vargas 333,Quitandinha, Petropolis, RJ CEP 26651470, Brad and Institute of Mathematics UFRJ, P.O.Box 68530, Rio de Janeiro, RJ Brasil.
Notes
1Pontificia Universidad CaMlica de Chile. Fscultad de Matemdticas. Cssilla 306, Corma, Santiago, Chile.
2National Laboratory of Scientific Computation, LNCCfCNPq. Rua Getulio Vargas 333,Quitandinha, Petropolis, RJ CEP 26651470, Brad and Institute of Mathematics UFRJ, P.O.Box 68530, Rio de Janeiro, RJ Brasil.