Dirichlet problem for the ion acoustic wave equation in two dimensions (Q1571278)

This paper is devoted to Dirichlet initial-boundary value problem for two-dimensional unsteady ion acoustic wave equation in an unmagnetized plasma in a plane domain with deleted curved segments. Such problems are not only of applied but also of theoretical interest, because they are generalizations of classical Keldysh-Lavrent'ev-Sedov problems for Laplace equation to the case of a mixed-type differential equation. The classical solvability of the problem is proved by methods of dynamic potential theory.