On hearing the shape of an arbitrary doubly-connected region in R2

E. M. E. Zayed

doi:10.1017/S0334270000006792

Abstract

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The basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region in R2 together with an impedance condition on its inner boundary and another impedance condition on its outer boundary, from the complete knowledge of the eigenvalues for the two-dimensional Laplacian using the asymptotic expansion of the spectral function for small positive t.

References

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Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Zayed, E. M. E. 1990. Hearing the shape of a general doubly connected domain in R3 with impedance boundary conditions. Journal of Mathematical Physics, Vol. 31, Issue. 10, p. 2361.

Zayed, E. M. E. and Younis, A. I. 1994. On hearing the shape of rectilinear regions. Journal of Mathematical Physics, Vol. 35, Issue. 7, p. 3490.

Zayed, E. M. E. 1995. An inverse problem for a general multiply connected bounded domain. Applicable Analysis, Vol. 59, Issue. 1-4, p. 553.

Zayed, E.M.E. and Abdel-Halim, I.H. 2001. The wave equation approach to the two-dimensional inverse problem for a general bounded domain with piecewise smooth mixed boundary conditions. Acta Mathematica Scientia, Vol. 21, Issue. 2, p. 171.

Zayed, E.M.E. and Abdel-Halim, I.H. 2001. The 3D inverse problem for waves with fractal and general annular bounded domain with piecewise smooth Robin boundary. Chaos, Solitons & Fractals, Vol. 12, Issue. 12, p. 2307.

Zayed, E.M.E. 2001. An inverse problem of the heat equation for a general multi-connected drum with applications in Physics. Chaos, Solitons & Fractals, Vol. 12, Issue. 10, p. 1861.

Zayed, E.M.E. 2001. Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain inR2with Robin Boundary Conditions. Applicable Analysis, Vol. 77, Issue. 1-2, p. 177.

Zayed, E.M.E. 2002. An inverse problem for a general annular-bounded domain in with mixed boundary conditions and its physical applications. Applied Mathematics and Computation, Vol. 129, Issue. 2-3, p. 237.

Zayed, E.M.E. and Abdel-Halim, I.H. 2002. An inverse problem of the wave equation for a general doubly connected region in with a finite number of piecewise smooth Robin boundary conditions. Applied Mathematics and Computation, Vol. 132, Issue. 1, p. 187.

Zayed, E. M. E. 2003. Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions: Further Results. Acta Mathematica Sinica, English Series, Vol. 19, Issue. 4, p. 679.

Zayed, E.M.E. 2003. Inverse problems for a general multi-connected bounded drum with applications in physics. Applied Mathematics and Computation, Vol. 139, Issue. 2-3, p. 231.

Zayed, E.M.E. 2003. The wave equation approach to an inverse problem for a general multi-connected domain in R2 with mixed boundary conditions. Applied Mathematics and Computation, Vol. 144, Issue. 2-3, p. 457.

Zayed, E.M.E. 2003. INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS. Acta Mathematica Scientia, Vol. 23, Issue. 1, p. 104.

Zayed, E.M.E. 2003. On hearing the shape of a general multi-connected vibrating membrane in with piecewise smooth positive functions in the Robin boundary conditions. Applied Mathematics and Computation, Vol. 135, Issue. 2-3, p. 361.

Zayed, E.M.E. 2004. Short-time asymptotics of the two-dimensional wave equation for an annular vibrating membrane with applications in the mathematical physics. Chaos, Solitons & Fractals, Vol. 19, Issue. 3, p. 679.

Zayed, E.M.E 2004. An inverse eigenvalue problem of the wave equation for a multi-connected region in R2 together with three different types of boundary conditions. Applied Mathematics and Computation, Vol. 154, Issue. 2, p. 361.

Zayed, E. M. E. 2004. Short-time Asymptotics of the Heat Kernel on Bounded Domain with Piecewise Smooth Boundary Conditions and Its Applications to an Ideal Gas. Acta Mathematicae Applicatae Sinica, English Series, Vol. 20, Issue. 2,

Zayed, E. M. E. 2004. The Asymptotics of the Two-Dimensional Wave Equation for a General Multi-Connected Vibrating Membrane with Piecewise Smooth Robin Boundary Conditions. Acta Mathematica Sinica, English Series, Vol. 20, Issue. 2, p. 209.

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On hearing the shape of an arbitrary doubly-connected region in R2

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