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Functional-integral equations and diffraction by a truncated wedge

Presented by: 
Mikhail Lyalinov
Friday 16th August 2019 - 15:00 to 15:30
INI Seminar Room 1
In this work we study diffraction of a plane incident wave in a complex 2D domain composed by two shifted angular domains having a part of their common boundary. The perfect (Dirichlet or Neumann) boundary conditions are postulated on the polygonal boundary of such compound domain. By means of the Sommerfeld-Malyuzhinets technique the boundary-value problem at hand is reduced to a non-standard systems of Malyuzhinets-type functional-integral equations and then to a Fredholm integral equation of the second kind. Existence and uniqueness of the solution for the diffraction problem is studied and is based on the Fredholm alternative for the integral equation. The far field asymptotics of the wave field is also addressed.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons