Крайові задачі для еволюційних рівнянь із виродженням за часовою змінною

Abstract

The dissertation is devoted to the study of the solvability of non-classical problems with local multipoint conditions, problems with Nicoletti conditions and problems with nonlocal two-point conditions on the selected variable and 2π-periodicity conditions on the remaining variables for a partial di erential equation of the Euler type. The interest of researchers in such problems is due both to the need to build a general theory of boundary value problems for partial di erential equations and to the fact that local multipoint and nonlocal problems arise in the mathematical description of a number of processes. In the general case, such problems are conditionally well-posed, and the study of their solvability is related to the problem of small denominators. The essence of the small denominator problem is that the coe cients of the Fourier series, which represent the solutions of the problems, contain denominators that can become arbitrarily close to zero for an in nite number of summation indices, which can cause the divergence of the series in the corresponding functional spaces.