Conditional stability and regularized solution of a boundary value problem for a system of mixed type equations in three-dimensional space

Abstract

In this paper, we study the initial-boundary value problem for the system of second-order mixed-type equations in three-dimensional space. An a priory estimate of the solution is obtained. Theorems of uniqueness and conditional stability are given. A regularized approximate solution is constructed in two cases. Estimates of effectiveness of the regularization method are obtained and formula for regularization parameter is derived.