Hearing the shape of a general doubly-connected domain in \(\mathbb{R}^ 3\) with mixed boundary conditions

DOI10.1007/BF00946176zbMath0778.35111OpenAlexW1970478469MaRDI QIDQ1178453

Elsayed M. E. Zayed

Publication date: 26 June 1992

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00946176

zbMATH Keywords

mixed boundary conditionsinverse eigenvalue problemdomain identificationarbitrary doubly- connected regionthree-dimensional Laplacian

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (16)

On hearing the shape of the three-dimensional multi-connected vibrating membrane with piecewise smooth boundary conditions ⋮ On hearing the shape of rectilinear regions ⋮ Higher dimensional inverse problem for a multi-connected bounded domain with piecewise smooth Robin boundary conditions and its physical applications. ⋮ Inverse problems for a general multi-connected bounded drum with applications in physics. ⋮ The wave equation approach for solving inverse eigenvalue problems of a multi-connected region in \({\mathbb R}^{3}\) with Robin conditions. ⋮ An inverse problem for a general doubly connected bounded domain in R³with a Finite Number of Piecewise Impedance Boundary Conditions ⋮ Asymptotic expansions of the heat kernel of the Laplacian for general annular bounded domains with Robin boundary conditions: Further results. ⋮ An inverse problem of the three-dimensional wave equation for a general annular vibrating membrane with piecewise smooth boundary conditions. ⋮ Short-time asymptotics of the heat kernel on bounded domain with piecewise smooth boundary conditions and its applications to an ideal gas ⋮ Higher dimensional inverse problem of the wave equation for a bounded domain with mixed boundary conditions ⋮ The 3D inverse problem of the wave equation for a general multi-connected vibrating membrane with a finite number of piecewise smooth boundary conditions. ⋮ An inverse problem for a general vibrating annular membrane in \(\mathbb R^ 3\) with its physical applications: further results. ⋮ An inverse problem for the three-dimensional multi-connected vibrating membrane with Robin boundary conditions. ⋮ Higher dimensional inverse problem of the wave equation for a general multi-connected bounded domain with a finite number of smooth mixed boundary conditions. ⋮ An inverse problem of the wave equation for a general annular drum in \({\mathbb R}^3\) with Robin boundary conditions ⋮ The 3D inverse problem for waves with fractal and general annular bounded domain with piecewise smooth Robin boundary

Cites Work

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• Heat equation for an arbitrary doubly-connected region in \(R^ 2\) with mixed boundary conditions
• Eigenvalues of the Laplacian for the third boundary value problem: An extension to higher dimensions
• An inverse eigenvalue problem for a general convex domain: an extension to higher dimensions
• Curvature and the eigenvalues of the Laplacian
• Eigenvalues of the Laplacian: an Extension to Higher Dimensions
• Eigenvalues of the Laplacian with Neumann boundary conditions

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