On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation

The authors investigate uniform stabilization of the solution of the second mixed problem in a cylindrical domain $(t>0)\times\Omega$ for a linear parabolic equation of second order. For a rather broad class of unbounded domains $\Omega\subset\mathbf R_n$ 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.