Nonlocal boundary value problem for a nonhomogeneous parabolic type equation with two degenerate lines

This work is devoted to the study of the conditional correctness of the nonlocal boundary value problem for a nonhomogeneous parabolic type equation with two degenerate lines. In this article we investigated well-posed of the problem depending of coefficients in conditions for a problem. In the case of ill-posed, based on the idea of A.N. Tikhonov, the conditional correctness of the problem are proved, namely, the theorems of uniqueness and conditional stability on the set of correctness are proved. For all cases we get a priori estimate of the solution we used the logarithmic convexity method and the results of the spectral problem considered by S.G. Pyatkov