An inverse problem of the heat equation for a general multi-connected drum with applications in physics.

DOI10.1016/S0960-0779(00)00114-4zbMath1064.35521MaRDI QIDQ5950562

Elsayed M. E. Zayed

Publication date: 2 January 2002

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

zbMATH Keywords

Dirichlet boundary conditionNeumann boundary conditioninverse spectral problemRobin boundary conditionideal gaseigenvalues of the negative Laplacianmulti-connected domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

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On hearing the shape of the three-dimensional multi-connected vibrating membrane with piecewise smooth boundary conditions, Short-time asymptotics of the two-dimensional wave equation for an annular vibrating membrane with applications in the mathematical physics, Short-time asymptotics of the heat kernel on bounded domain with piecewise smooth boundary conditions and its applications to an ideal gas, An inverse problem for a general vibrating annular membrane in \(\mathbb R^ 3\) with its physical applications: further results., The 3D inverse problem for waves with fractal and general annular bounded domain with piecewise smooth Robin boundary

Cites Work

• Hearing the shape of a general convex domain
• 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
• An inverse eigenvalue problem for an arbitrary multiply connected bounded region in \(R^ 2\)
• Curvature and the eigenvalues of the Laplacian
• Distribution of eigenfrequencies for the wave equation in a finite domain. I.: Three-dimensional problem with smooth boundary surface
• A study of certain Green's functions with applications in the theory of vibrating membranes
• 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
• 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 an arbitrary doubly-connected region in R²
• 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?
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