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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:TALK133600@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 is proposed. It requires mapping the wedge
  domain into a right-angled structure and applying two Laplace transforms.
  The main feature of the method is that the second integral transform para
 meter is a specific root of the characteristic polynomial of the ordinary 
 differential operator resulting from the transformed PDE. For convex domai
 ns (concave obstacles)\, the problems reduce to scalar and order-2 vector 
 Riemann-Hilbert problems. When the wedge is concave (a convex obstacle)\, 
 the acoustic problem is transformed into an order-3 Riemann-Hilbert proble
 m. The order-2 and 3 vector Riemann-Hilbert problems are solved by recasti
 ng them as scalar Riemann-Hilbert problems on Riemann surfaces. Exact solu
 tions of the problems are determined. Existence and uniqueness issues are 
 discussed.
LOCATION:Seminar Room 1\, Newton Institute
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