Conditional Correctness of the Initial-Boundary Value Problem for The System of Second Order Mixed Type Equations

Abstract

In this paper, we investigate the ill-posed initial boundary value problem for the system of mixed type equations. A priori estimate of solution is obtained with the method of logarithmic convexity. The theorems of uniqueness and conditional stability are proved on the set of correctness of the solution. An approximate solution to the problem is constructed by the regularization method. We calculate an estimate for efficiency of the norm of the difference between exact and approximate solutions.