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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Diffraction by wedges: higher order boundary condi
tions\, integral transforms\, vector Riemann-Hilbe
rt problems\, and Riemann surfaces - Yuri Antipov
(Louisiana State University)
DTSTART;TZID=Europe/London:20191101T133000
DTEND;TZID=Europe/London:20191101T143000
UID:TALK133597AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133597
DESCRIPTION:Acoustic and electromagnetic diffraction by a wedg
e is modeled by one and two Helmholtz equations co
upled by boundary conditions. When the wedge walls
are membranes or elastic plates\, the impedance b
oundary conditions have derivatives of the third o
r fifth order\, respectively. A new method of inte
gral transforms for right-angled wedges is propose
d. It is based on application of two Laplace trans
forms. The main feature of the method is that the
second integral transform parameter is a specific
root of the characteristic polynomial of the ordin
ary differential operator resulting from the trans
formed PDE by the first Laplace transform. For con
vex domains (concave obstacles)\, the problems red
uce to scalar and order-2 vector Riemann-Hilbert p
roblems. When the wedge is concave (a convex obsta
cle)\, the acoustic problem is transformed into an
order-3 Riemann-Hilbert problem. The order-2 and
3 vector Riemann-Hilbert problems are solved by re
casting them as scalar Riemann-Hilbert problems on
Riemann surfaces. Exact solutions of the problems
are determined. Existence and uniqueness issues a
re discussed.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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