On stabilization of solutions of the Cauchy problem for a parabolic equation with lower-order coefficients期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:

V N Denisov

Abstract:

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

$\Delta u + c(x,t)u - u_t = 0 for x \in {\mathbb{R}}^N ,t > 0,$

under which its solution satisfying the initial condition

$\left. u \right|_{t = 0} = u_0 (x) for x \in {\mathbb{R}}^N$

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

$\mathop {\lim }\limits_{t \to \infty } u(x,t) = 0,$

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 $e^{a\left| x \right|^b }$ with a > 0 and b < 0 at infinity. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 79–97, 2006.

Keywords:

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