FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 79-97

On stabilization of solutions of the Cauchy problem for a parabolic equation with lower-order coefficients

V. N. Denisov

Abstract

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In the paper, we study the sufficient conditions for the lower-order coefficient of the parabolic equation

under which its solution satisfying the initial condition

stabilizes to zero, i.e., there exists the limit

uniform in $x$ from every compact set $K$ in $$R^N for any function $u$₀(x) belonging to a certain uniqueness class of the problem considered and growing not rapidly than $ea\; |x|b$ with $a\; >\; 0$ and $b\; >\; 0$ at infinity.

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Last modified: February 17, 2007