Geodesic
On the behaviour of solutions of parabolic equations for large values of time
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 4, pp. 721-790 
V. N. Denisov. On the behaviour of solutions of parabolic equations for large values of time. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 4, pp. 721-790. http://geodesic.mathdoc.fr/item/RM_2005_60_4_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is a survey of classical and new results on stabilization of solutions of the Cauchy problem and mixed problems for second-order linear parabolic equations. Proofs are given for some new results about exact sufficient conditions on the behaviour of lower-order coefficients of the parabolic equation; these conditions ensure stabilization of a solution of the Cauchy problem for the parabolic equation in the class of bounded or increasing initial functions.