Spectral Properties of an Acoustic Boundary Condition

Journal Article

A boundary condition is studied for the wave equation occurring in theoretical acoustics. The initial value problem in a bounded domain is solved by semigroup methods in a Hilbert space of data with finite energy. A description of the spectrum of the semigroup generator A is then obtained. Unlike the generators associated with the usual boundary conditions, which have compact resolvent and spectrum consisting of discrete eigenvalues, A always has essential spectrum. Moreover, if the parameters occurring in the boundary condition are constant, there are sequences of eigenvalues converging to the essential spectrum.

Duke Authors

Cited Authors

  • Beale, JT

Published Date

  • 1976

Published In

  • Indiana University Mathematics Journal

Volume / Issue

  • 25 / 9

Start / End Page

  • 895 - 917