Three-dimensional integro-multipoint boundary value problem for loaded Volterra-hyperbolic integro-differential equations of Bianchi type

Abstract

In this paper the combined three-dimensional non-local boundary value problem with integro-multipoint conditions for loaded volterra-hyperbolic integro-differential equation of Bianchi type is explored. The matter of principle is the fact, that the considered equation has discontinuous coefficients which satisfy only some conditions of P-integrability type and boundedness, i.e. the considered hyperbolic differential operator has no traditional conjugate operator. In particular, for example, Riemann function under Goursat conditions for such equation cannot be constructed by classical method of characteristics.

Keywords

• three-dimensional non-local boundary problem
• loaded integro-differential equations
• hyperbolic equation
• equations with discontinuous coefficients