Stabilization of Solution to the Cauchy Problem for a Parabolic Equation with Lower Order Coefficients and an Exponentially Growing Initial Function

For the coefficients of lower order terms of a second-order parabolic equation, we obtain sharp sufficient conditions under which the solution of the Cauchy problem stabilizes to zero uniformly in $x$ on each compact set $K$ in $\mathbb R^N$ for any exponentially growing initial function.