The Wiener-Hopf equations and the mathematical theory of diffraction (Q1904020)

The author considers the Dirichlet or Neumann problem for the quarter- plane diffraction problem. Here the Dirichlet problem may be formulated as follows: \((\Delta+ k^2) u=0\), \(u(x)\in \mathbb{R}^2 \setminus \overline {\Gamma}^+\), \(u(x')= g(x')\), \(x'\in \Gamma^+\), where \(\Gamma^+= \{x\in \mathbb{R}^3\), \(x_3=0\), \(x_2> |x_1|\}\), \(k= k_1+ ik_2\), \(k_2>0\). The author investigates a pseudodifferential equation to which the considered problem may be reduced and gives an explicit solution in the simplest case.