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Tr. Semim. im. I. G. Petrovskogo, 2019, Issue 32, Pages 220–238 (Mi tsp108)  

On the stabilization of solutions of nonlinear parabolic equations with lower-order derivatives

A. A. Kon'kov


Abstract: For parabolic equations of the form
$$ \frac{\partial u}{\partial t}- \sum_{i,j=1}^n a_{ij} (x, u) \frac{\partial^2 u}{\partial x_i \partial x_j} + f (x, u, D u) = 0 in {\mathbb R}_+^{n+1}, $$
where ${\mathbb R}_+^{n+1} = {\mathbb R}^n \times (0, \infty)$, $n \ge 1$, $D = (\partial / \partial x_1, \ldots, \partial / \partial x_n)$, and $f$ satisfies some constraints, we obtain conditions that ensure the convergence of any its solution to zero as $t \to \infty$.

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English version:
Journal of Mathematical Sciences (New York), 2020, 244:2, 254–266

UDC: 517.95

Citation: A. A. Kon'kov, “On the stabilization of solutions of nonlinear parabolic equations with lower-order derivatives”, Tr. Semim. im. I. G. Petrovskogo, 32, 2019, 220–238; J. Math. Sci. (N. Y.), 244:2 (2020), 254–266

Citation in format AMSBIB
\Bibitem{Kon19}
\by A.~A.~Kon'kov
\paper On the stabilization of solutions of nonlinear parabolic equations with lower-order derivatives
\serial Tr. Semim. im. I. G. Petrovskogo
\yr 2019
\vol 32
\pages 220--238
\mathnet{http://mi.mathnet.ru/tsp108}
\elib{https://elibrary.ru/item.asp?id=43213044}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 244
\issue 2
\pages 254--266
\crossref{https://doi.org/10.1007/s10958-019-04617-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85075623965}


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