The question about the possibility of increasing the convergence of this solution for $t → +0$ in the case when the initial distribution $f$ has local positive good properties is investigated. This question is concidered for regular solutions of the Shilov-type parabolic equations with variable coefficients of limited smoothness and non-negative genius, which in the initial hyperplane $t = 0$  have generalized boundary date of distributions by the Gelfand-Shilov type. The solution of the question has the compact uniform convergence to zero. This convergence is proven by conditions that the order of smoothness of the coefficients is not lower than the order of the equation.This effect of increasing the convergence of the solution is reseached for equations with parabolicity of Petrovs’kyy in the case when the initial distribution $f$  on a certain part of the hyperplane is continuous or continuously differentiable to a certain order by a function.

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