Stabilization of the solution to the cauchy problem for a parabolic equation with nonzero lower order coefficients in classes of increasing initial functions.

The article analyzes enough conditions on the lower order coefficients of the parabolic equations in the second-order. It discusses the solution of the Cauchy problem in classes of rising initial functions stables x-uniformly to zero on each compact set K ∈ R^N. It presents the reality of coefficients α_ik = α_ki (i, k = 1, 2, ..., N) and the satisfaction of the uniform parabolicity conditions; Ǝ there exist constants ɻ₀ 0 and ɻ₁.