The Existence and Uniqueness of a New Boundary Value Problem (Type of Problem “E”) for Linear System Equations of the Mixed Hyperbolic-Elliptic Type in the Multivariate Dimension with the Changing Time Direction

Abstract

The existence and uniqueness of the boundary value problem for linear systems equations of the mixed hyperbolic-elliptic type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “$\epsilon$-regularizing” continuation by the parameter and by means of prior estimates, the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev space.