This note is related to the famous question raised by Mark Kac and concerning the determination of the shape of the drum by the eigenvalues of its governing equation. Here, we allow the drum to be composed by several different types of membranes and we consider the problem of hearing the composition of the drum, starting from the eigenvalues of numerical approximations of the related equation. Some key tools, taken from asymptotic linear algebra, are reported and extended, and allow somehow to answer to the question in the positive.

Can one hear the composition of a drum?

SERRA CAPIZZANO, STEFANO;
2006-01-01

Abstract

This note is related to the famous question raised by Mark Kac and concerning the determination of the shape of the drum by the eigenvalues of its governing equation. Here, we allow the drum to be composed by several different types of membranes and we consider the problem of hearing the composition of the drum, starting from the eigenvalues of numerical approximations of the related equation. Some key tools, taken from asymptotic linear algebra, are reported and extended, and allow somehow to answer to the question in the positive.
2006
Clustering; Distribution eigenvalue formula; PD Es and Finite Difference
Holmgren, S.; SERRA CAPIZZANO, Stefano; Sundqvist, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1494924
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