GENERALIZED SOLUTIONS OF NONSTATIONARY BOUNDARY VALUE PROBLEMS FOR THE KLEIN-GORDON-FOCK EQUATION

Abstract

The article deals with non-stationary boundary value problem for the Klein-Gordon-Fock equation un- der Dirichlet or Neumann conditions at the boundary of definition domain. On the basis of the method of gener- alized functions the method of boundary integral equations for solving them is designed. The dynamic analogues of Green formulas in the space of generalized functions are obtained, and its regular integral representations in the plane and three-dimensional cases are built. The singular boundary integral equations for solving the non- stationary boundary value problems have been constructed.