On Stabilization of the Solution of the Cauchy Problem for a Parabolic Equation with a Lower Order Coefficient and a Growing Initial Function

The paper deals with the study of sufficient conditions on the coefficients of a second-order partial differential equation, ensuring the stabilization to zero of the solution of the Cauchy problem uniformly in x on any compact set K ⊂ ℝN for any continuous initial function u0(x), growing at infinity not faster than some power of |x|m, m > 0.