The wave equation approach to an inverse problem for a general multi-connected domain in \(\mathbb{R}^{2}\) with mixed boundary conditions.

DOI10.1016/S0096-3003(02)00420-4zbMath1033.35154MaRDI QIDQ1405074

Elsayed M. E. Zayed

Publication date: 25 August 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

wave equationspectral functioninverse spectral problemeigenvalues of the negative Laplaciandomain reconstructionDirichlet Neumann and Robin boundary conditionsmulti-connected bounded domain

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Wave equation (35L05)

Related Items (1)

An inverse eigenvalue problem of the wave equation for a multi-connected region in \(\mathbb{R}^{2}\) together with three different types of boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hearing the shape of a general convex domain
• Trace formulae for the eigenvalues of the Laplacian
• Heat equation for an arbitrary doubly-connected region in \(R^ 2\) with mixed boundary conditions
• An inverse eigenvalue problem for a general convex domain
• Can one hear the dimension of a fractal?
• The asymptotics of the heat equation for a boundary value problem
• The spectral function of an elliptic operator
• Curvature and the eigenvalues of the Laplacian
• A study of certain Green's functions with applications in the theory of vibrating membranes
• Hearing the shape of an annular drum
• Heat Equation for an Arbitrary Multiply-Connected Region in R² with Impedance Boundary Conditions
• An inverse problem for a general convex domain with impedance boundary conditions
• Eigenvalues of the Laplacian with Neumann boundary conditions
• Eigenvalues of the Laplacian for the third boundary value problem
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
• One cannot hear the shape of a drum
• On hearing the shape of rectilinear regions
• On hearing the shape of an arbitrary doubly-connected region in R²
• Eigenvalues of the Laplacian for rectilinear regions
• An inverse problem for a general multiply connected bounded domain
• On hearing the shape of a bounded domain with Robin boundary conditions
• Can One Hear the Shape of a Drum?
• The asymptotics of the heat semigroup for a general bounded domain with mixed boundary conditions
• Short-time asymptotics of the trace of the wave operator for a general annular drum in \(\mathbb{R}^2\) with Robin boundary conditions.
• The wave equation approach to the two-dimensional inverse problem for a general bounded domain with piecewise smooth mixed boundary conditions

This page was built for publication: The wave equation approach to an inverse problem for a general multi-connected domain in \(\mathbb{R}^{2}\) with mixed boundary conditions.