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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.

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

Bibliographic databases:

UDC: 517.9
Received: 14.04.1967

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}


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