Publications [#243338] of J. Thomas Beale
- BEALE, JT, ACOUSTIC SCATTERING FROM LOCALLY REACTING SURFACES,
Indiana University Mathematics Journal, vol. 26 no. 2
pp. 199-222 [doi]
(last updated on 2019/11/19)
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 so-called 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 pre-compact sets with respect to local energy. As a consequence, the local decay of arbitrary solutions of finite energy is established.