Heat equation for an arbitrary doubly-connected region in \(R^ 2\) with mixed boundary conditions

DOI10.1007/BF00945010zbMath0704.35133MaRDI QIDQ916917

Elsayed M. E. Zayed

Publication date: 1989

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

zbMATH Keywords

Laplace operatormixed boundary conditionsdoubly-connected region

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) Inverse problems for PDEs (35R30)

Related Items (18)

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 ⋮ The asymptotics of the two-dimensional wave equation for a general multi-connected vibrating membrane with piecewise smooth Robin boundary conditions ⋮ On hearing the shape of rectilinear regions ⋮ An inverse problem for a general multiply connected bounded domain ⋮ The wave equation approach to an inverse problem for a general multi-connected domain in \(\mathbb{R}^{2}\) with mixed boundary conditions. ⋮ Inverse problems for a general multi-connected bounded drum with applications in physics. ⋮ Asymptotic expansions of the heat kernel of the Laplacian for general annular bounded domains with Robin boundary conditions: Further results. ⋮ Short-time asymptotics of the two-dimensional wave equation for an annular vibrating membrane with applications in the mathematical physics ⋮ Hearing the shape of a general doubly-connected domain in \(\mathbb{R}^ 3\) with mixed boundary conditions ⋮ Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain inR²with Robin Boundary Conditions ⋮ The asymptotics of the heat semigroup for a general bounded domain with mixed boundary conditions ⋮ 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 of the heat equation for a general multi-connected drum with applications in physics. ⋮ Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain inR²with Robin Boundary Conditions ⋮ An inverse problem for a general annular-bounded domain in \(\mathbb R^ 2\) with mixed boundary conditions and its physical applications. ⋮ An inverse problem of the wave equation for a general doubly connected region in \(\mathbb R^2\) with a finite number of piecewise smooth Robin boundary conditions. ⋮ On hearing the shape of a general multi-connected vibrating membrane in \(\mathbb R^2\) with piecewise smooth positive functions in the Robin boundary conditions. ⋮ The 3D inverse problem for waves with fractal and general annular bounded domain with piecewise smooth Robin boundary

Cites Work

• Unnamed Item
• Trace formulae for the eigenvalues of the Laplacian
• An inverse eigenvalue problem for a general convex domain
• The asymptotics of the heat equation for a boundary value problem
• Curvature and the eigenvalues of the Laplacian
• An asymptotic expansion for the heat equation
• A study of certain Green's functions with applications in the theory of vibrating membranes
• Hearing the shape of an annular drum
• Eigenvalues of the Laplacian with Neumann boundary conditions
• Eigenvalues of the Laplacian for the third boundary value problem
• Eigenvalues of the Laplacian for rectilinear regions
• Can One Hear the Shape of a Drum?

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