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

$$Du +
c(x,t)u - u_{t} = 0
for x Î
**R**^{N}, t > 0,
under which its solution satisfying the initial condition

$u|$_{t=0} = u_{0}(x)
for x Î
**R**^{N},
stabilizes to zero, i.e., there exists the limit

$lim$_{t → ¥} u(x,t) = 0,
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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06406h.htm

Last modified: February 17, 2007