7 марта в 18:00 состоится заседание семинара кафедры Высшей математики и математической физики, ПОМИ, ауд. 203.
Докладчик: М.А. Лялинов
Тема: Акустическое рассеяние на полубесконечном секторе с импедансными краевыми условиями
In this work we study the problem of diffraction of an acoustic plane wave by a semi-infinite angular sector with impedance boundary conditions on its surface. It is studied by means of incomplete separation of variables. With the aid of Watson–Bessel integral representation the problem is reduced to a boundary value problem on the unit sphere with an operator-impedance boundary condition on a cut of the sphere. The latter problem is further studied by means of the traditional methods of extensions of sectorial sesquilinear forms. The Sommerfeld integral representation is obtained from that of Watson–Bessel with the aim to develop the far-field asymptotics. Analytic properties of the corresponding Sommerfeld transformant are also discussed. For a narrow impedance sector, an asymptotic formula for the diffraction coefficient of the spherical wave propagating from the vertex is derived.