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Volume 7, Issue 3
The Wave Equation Approach to Robbin Inverse Problems for a Doubly-Connected Region: An Extension to Higher Dimensions

E. M. E. Zayed

J. Comp. Math., 7 (1989), pp. 301-312.

Published online: 1989-07

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  • Abstract

The spectral function $\hatμ(t)=\sum\limits_{j=1}^\infty e^{-itλ^{\frac{1}{2}}_j}$ where $\{λ_j\}^\infty_{j=1}$ are the eigenvalues of the three-dimensional Laplacian is studied for a variety of domains, where $- \infty＜t＜\infty$ and $i=\sqrt{-1}$. The dependence of $\hat{\mu}(t)$ on the connectivity of a domain and the impedance boundary condition (Robbin conditions) are analyzed. Particular attention is given to the spherical shell together with Robbin boundary conditions on its surface.

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@Article{JCM-7-301, author = {E. M. E. Zayed}, title = {The Wave Equation Approach to Robbin Inverse Problems for a Doubly-Connected Region: An Extension to Higher Dimensions}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {3}, pages = {301--312}, abstract = {

The spectral function $\hatμ(t)=\sum\limits_{j=1}^\infty e^{-itλ^{\frac{1}{2}}_j}$ where $\{λ_j\}^\infty_{j=1}$ are the eigenvalues of the three-dimensional Laplacian is studied for a variety of domains, where $- \infty＜t＜\infty$ and $i=\sqrt{-1}$. The dependence of $\hat{\mu}(t)$ on the connectivity of a domain and the impedance boundary condition (Robbin conditions) are analyzed. Particular attention is given to the spherical shell together with Robbin boundary conditions on its surface.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9478.html} }
TY - JOUR T1 - The Wave Equation Approach to Robbin Inverse Problems for a Doubly-Connected Region: An Extension to Higher Dimensions AU - E. M. E. Zayed JO - Journal of Computational Mathematics VL - 3 SP - 301 EP - 312 PY - 1989 DA - 1989/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9478.html KW - AB -

The spectral function $\hatμ(t)=\sum\limits_{j=1}^\infty e^{-itλ^{\frac{1}{2}}_j}$ where $\{λ_j\}^\infty_{j=1}$ are the eigenvalues of the three-dimensional Laplacian is studied for a variety of domains, where $- \infty＜t＜\infty$ and $i=\sqrt{-1}$. The dependence of $\hat{\mu}(t)$ on the connectivity of a domain and the impedance boundary condition (Robbin conditions) are analyzed. Particular attention is given to the spherical shell together with Robbin boundary conditions on its surface.

E. M. E. Zayed. (1989). The Wave Equation Approach to Robbin Inverse Problems for a Doubly-Connected Region: An Extension to Higher Dimensions. Journal of Computational Mathematics. 7 (3). 301-312. doi:
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