The asymptotics of the heat semigroup for a general bounded domain with mixed boundary conditions

DOI10.1007/S101140000058zbMath0973.35089OpenAlexW2069718024MaRDI QIDQ5925956

Elsayed M. E. Zayed

Publication date: 27 November 2001

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s101140000058

zbMATH Keywords

finite number of Dirichlet, Neumann and Robin conditionsinverse problemsmall-time asymptotics

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) General topics in linear spectral theory for PDEs (35P05) One-parameter semigroups and linear evolution equations (47D06)

Related Items (8)

On hearing the shape of the three-dimensional multi-connected vibrating membrane with piecewise smooth boundary conditions ⋮ The wave equation approach to an inverse problem for a general multi-connected domain in \(\mathbb{R}^{2}\) with mixed 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 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. ⋮ An inverse problem for the three-dimensional multi-connected vibrating membrane with Robin boundary conditions. ⋮ 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
• 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
• An inverse problem for a general convex domain with impedance boundary conditions
• Eigenvalues of the Laplacian with Neumann boundary conditions
• Can One Hear the Shape of a Drum?
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