This work is devoted to the study of a nonlocal boundary value problem for a system of two-dimensional parabolic equations with changing direction of time. A priori estimate is obtained for the solution of the problem under consideration, and theorems on stability and conditional stability are proved depending on the parameters of the nonlocal condition. As a result, the uniqueness of the solution to the problem is presented.
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Fayazov, Kudratillo and Khajiev, Ikrombek
"Nonlocal boundary value problem for a system of mixed type equations with a line of degeneration,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 4:
1, Article 2.