Abstract
We study the correctness of a problem with multipoint conditions with respect to the time variable and conditions of the Dirichlet type with respect to spatial coordinates for a class of equations parabolic by Petrovskii with coefficients variable in spatial coordinates in a bounded cylindrical domain. The conditions for existence and uniqueness of solution of the problem are determined. A metric theorem of lower bounds for small denominators arising in the construction of the solution is proved.
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