AN INVERSE PROBLEM FOR A GENERAL DOUBLY-CONNECTED BOUNDED DOMAIN: AN EXTENSION TO HIGHER DIMENSIONS

Authors

  • E. M. E. ZAYED Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

DOI:

https://doi.org/10.5556/j.tkjm.28.1997.4305

Keywords:

Inverse problem, spectral function, eigenvalues, doubly-connected domain, hearing the shape of a drum

Abstract

The spectral function $\Theta(t)=\sum_{\nu=1}^\infty \exp(-t\lambda_\nu)$, where $\{\lambda_\nu\}_{\nu=1}^\infty$ are the eigenvalues of the negative Laplacian $-\nabla^2=-\sum_{i=1}^3(\frac{\partial}{\partial x_i})^2$ in the $(x^1, x^2, x^3)$-space, is studied for an arbitrary doubly connected bounded domain $\Omega$ in $R^3$ together with its smooth inner bounding surface $\tilde S_1$ and its smooth outer bounding surface $\tilde S_2$, where piecewise smooth impedance boundary conditions on the parts $S_1^*$, $S_2^*$ of $\tilde S_1$ and $S_3^*$, $S_4^*$ of $\tilde S_2$ are considered, such that $\tilde S_1=S_1^*\cup S_2^*$ and $\tilde S_2=S_3^*\cup S_4^*$.

References

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Published

1997-12-01

How to Cite

ZAYED, E. M. E. (1997). AN INVERSE PROBLEM FOR A GENERAL DOUBLY-CONNECTED BOUNDED DOMAIN: AN EXTENSION TO HIGHER DIMENSIONS. Tamkang Journal of Mathematics, 28(4), 277-295. https://doi.org/10.5556/j.tkjm.28.1997.4305

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Papers