Iv. Andronov, APPLICATION OF ZERO-RANGE MODELS TO THE PROBLEM OF DIFFRACTION BY A SMALL HOLE IN ELASTIC PLATE, Journal of mathematical physics, 34(6), 1993, pp. 2226-2241
The theory of zero-range potentials is applied to the boundary-contact
acoustics problem of diffraction by small round holes in elastic plat
es. First the set of all point models of small inhomogeneities, repres
ented by zero-range potentials in L2 is constructed. Then the problem
of choosing the model corresponding to the examined diffraction proble
m is simplified by decomposition of the model into two components. One
corresponds to the case of an absolutely rigid plate, the other to th
e case of an isolated plate. Problems of diffraction for both componen
ts can be solved exactly by variables separation method. Comparing the
far field asymptotics for these problems with that produced by point
models one can find the parameters of the zero-range potential. When t
he potential is fixed the solution, being a number of leading terms in
the asymptotical on the small radius of the hole decomposition of far
field, is explicitly calculated.