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. Boundary value problems for equations of mixed type are used in problems of gas dynamics, the theory of infinitesimal bending of surfaces, mathematical biology and other fields. 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, which is stable on the set of correctness. Estimates of effectiveness of the regularization method are obtained and formula for regularization parameter is derived.

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DOI

10.2298/fil2419773k

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