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SUMMARY:Diffraction by wedges: higher order boundary conditions\, integral
  transforms\, vector Riemann-Hilbert problems\, and Riemann surfaces - Yur
 i Antipov (Louisiana State University)
DTSTART:20191101T133000Z
DTEND:20191101T143000Z
UID:TALK133597@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Acoustic and electromagnetic diffraction by a wedge is modeled
  by one and two Helmholtz equations coupled by boundary conditions. When t
 he wedge walls are membranes or elastic plates\, the impedance boundary co
 nditions have derivatives of the third or fifth order\, respectively. A ne
 w method of integral transforms for right-angled wedges is proposed. It is
  based on application of two Laplace transforms. The main feature of the m
 ethod is that the second integral transform parameter is a specific root o
 f the characteristic polynomial of the ordinary differential operator resu
 lting from the transformed PDE by the first Laplace transform. For convex 
 domains (concave obstacles)\, the problems reduce to scalar and order-2 ve
 ctor Riemann-Hilbert problems. When the wedge is concave (a convex obstacl
 e)\, the acoustic problem is transformed into an order-3 Riemann-Hilbert p
 roblem. 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
  are discussed.
LOCATION:Seminar Room 1\, Newton Institute
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