This article is cited in 53 papers

On the behaviour of solutions of parabolic equations for large values of time

V. N. Denisov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: 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.

UDC: 517.95

MSC: Primary 35K15, 35K20, 35B40; Secondary 35K05, 35B35

DOI: 10.4213/rm1448

 English version: Russian Mathematical Surveys, 2005, 60:4, 721–790

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