Geodesic
On the behavior, for large time values, of nonnegative solutions of the second mixed problem for a parabolic equation
Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 195-209 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author studies the behavior, for large time values $t$, of a nonnegative solution of the second mixed problem for a uniformly parabolic equation $$ \frac{\partial u(x,t)}{\partial t}=\sum_{i,j=1}^n\frac\partial{\partial x_i}\biggl(a_{ij}(x,t)\frac{\partial u(x,t)}{\partial x_j}\biggr) $$ in a cylindrical domain $\Omega\times\{t>0\}$, where $\Omega$ is an unbounded domain in $\mathbf R^n$. It is shown that for a certain class of unbounded domains $\Omega$, the behavior of the solution of the problem as $t\to\infty$ is determined by the behavior, for large values of the parameter $R$, of the means of the initial function over the sets $\{x\in\Omega:|x-\xi|, $\xi\in\Omega$, $R>0$. Bibliography: 8 titles. 
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     title = {On the behavior, for large time values, of nonnegative solutions of the second mixed problem for a~parabolic equation},
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A. V. Lezhnev. On the behavior, for large time values, of nonnegative solutions of the second mixed problem for a parabolic equation. Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 195-209. http://geodesic.mathdoc.fr/item/SM_1987_57_1_a12/

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