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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1968, Volume 3, Issue 1, Pages 85–92 (Mi mz6655)

The stabilization of the solutions of certain parabolic equations and systems

M. I. Freidlin

M. V. Lomonosov Moscow State University

Abstract: This paper concerns the investigation of the stabilization of solutions of the Cauchy problem for a system of equations of the form $\frac{\partial u}{\partial t}=\Delta u+F_1(u,v)$. It is proved that under certain assumptions the behavior of solutions as $t\to\infty$ is determined by mutual arrangement of the set of initial conditions $\{(u,v):u=f_1(x), v=f_2(x), x\in R^n\}$ and the trajectories of the system of ordinary differential equations $\frac{du}{dt}=F_1(u,v)$. The question of stabilization of the solutions of a single quasilinear parabolic equation is also considered.

Full text: PDF file (487 kB)

English version:
Mathematical Notes, 1968, 3:1, 50–54

Bibliographic databases:

UDC: 517.9

Citation: M. I. Freidlin, “The stabilization of the solutions of certain parabolic equations and systems”, Mat. Zametki, 3:1 (1968), 85–92; Math. Notes, 3:1 (1968), 50–54

Citation in format AMSBIB
\Bibitem{Fre68} \by M.~I.~Freidlin \paper The stabilization of the solutions of certain parabolic equations and systems \jour Mat. Zametki \yr 1968 \vol 3 \issue 1 \pages 85--92 \mathnet{http://mi.mathnet.ru/mz6655} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=222484} \zmath{https://zbmath.org/?q=an:0162.15303} \transl \jour Math. Notes \yr 1968 \vol 3 \issue 1 \pages 50--54 \crossref{https://doi.org/10.1007/BF01386966}