ON UNIFORM STABILIZATION OF THE SOLUTION OF THE SECOND MIXED PROBLEM FOR A SECOND ORDER PARABOLIC EQUATION

Abstract

The authors investigate uniform stabilization of the solution of the second mixed problem in a cylindrical domain for a linear parabolic equation of second order. For a rather broad class of unbounded domains a sharp estimate of the Green function for the problem in question is established, and a condition on the initial function is found which is necessary and sufficient for uniform stabilization of the solution.Bibliography: 14 titles.