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We present a general method of solving the Cauchy problem for a linearparabolic partial differential equation of evolution type with variablecoefficients and demonstrate it on the equation with derivatives of orders two,one and zero. The method is based on the Chernoff approximation procedureapplied to a specially constructed shift operator. It is proven thatapproximations converge uniformly to the exact solution.

Approximations to the solution of Cauchy problem for a linear evolution equation via the space shift operator (second-order equation example)