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Publications [#243337] of J. Thomas Beale

Papers Published

  1. Beale, JT, Spectral Properties of an Acoustic Boundary Condition, Indiana University Mathematics Journal, vol. 25 no. 9 (1976), pp. 895-917
    (last updated on 2019/11/13)

    Abstract:
    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.