Gellerstedt Type Directional Derivative Problem for an Equation of the Mixed Type with a Spectral Parameter

Abstract

For a two-dimensional equation of the mixed type with a spectral parameter, we consider a boundary value problem with a directional derivative on a half-circle and the Dirichlet condition on characteristic segments. The problem is reduced to an integro-differential equation for the boundary value of the conjugate function on the half-circle. It is shown that this equation is uniquely solvable and the leading part of the inverse operator can be found in closed form.