BOUNDARY POINT PROBLEM FOR A SYSTEM OF SECOND-ORDER NONCLASSICAL EQUATIONS

Abstract

This article studies a boundary value problem for a system of second-order nonclassical equations. The problem is considered together with initial, boundary, and constraint conditions. The solution of the problem is analyzed from the point of view of existence, uniqueness, and conditional stability. Also, an a priori estimate is obtained for the solution and the conditional correctness set of the problem is determined. Based on the definition of J. Adamard, the general ill-posedness of the problem is shown. In addition, in this work, the spectral problem is also analyzed and its eigenvalues and eigenfunctions are determined. It is proved that these eigenfunctions form a Riesz basis, and an approximate solution of the problem is constructed on their basis by the regularization method. The results of the research serve as an important theoretical basis for obtaining stable solutions for ill-posed problems