Geodesic
On uniform stabilization of the solution of the second mixed problem for a~second order parabolic equation
Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 141-162

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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. 
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     title = {On uniform stabilization of the solution of the second mixed problem for a~second order parabolic equation},
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A. K. Gushchin; V. P. Mikhailov; Yu. A. Mikhailov. On uniform stabilization of the solution of the second mixed problem for a~second order parabolic equation. Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 141-162. http://geodesic.mathdoc.fr/item/SM_1987_56_1_a9/