Math @ Duke

Publications [#243338] of J. Thomas Beale
Papers Published
 BEALE, JT, ACOUSTIC SCATTERING FROM LOCALLY REACTING SURFACES,
Indiana University Mathematics Journal, vol. 26 no. 2
(1977),
pp. 199222 [doi]
(last updated on 2019/04/22)
Abstract: A theory is developed for scattering from surfaces that are nonporous and locally reacting in the sense that wave motion along the surface is negligible. It is assumed that a small part of the surface reacts to the excess pressure due to the wave like a resistive harmonic oscillator. This boundary condition differs from others for the acoustic equation in that it does not have the socalled coercive property. However, with certain assumptions on the parameters occurring in the boundary behavior, it is possible to find a special class of initial data, dense in the energy norm, whose solutions form precompact sets with respect to local energy. As a consequence, the local decay of arbitrary solutions of finite energy is established.


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