Echoes and glimpses of a distant drum

DOI10.7494/OpMath.2020.40.6.737zbMath1468.35003MaRDI QIDQ4987025

John W. Turner

Publication date: 28 April 2021

Published in: Opuscula Mathematica (Search for Journal in Brave)

zbMATH Keywords

inverse methodsDuhamel methodKac drum problemrestriction to a polygonal boundary

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) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) History of differential geometry (53-03) History of partial differential equations (35-03)

Cites Work

• Partial differential equations. 4th ed
• The asymptotics of the heat equation for a boundary value problem
• Curvature and the eigenvalues of the Laplacian
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• A study of certain Green's functions with applications in the theory of vibrating membranes
• The asymptotic solution of linear differential equations of the second order for large values of a parameter
• Heat Equation for a Region in R² with a Polygonal Boundary
• One cannot hear the shape of a drum
• Can One Hear the Shape of a Drum?
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds