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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 3, Pages 433–444 (Mi zvmmf500)  
This article is cited in 13 scientific papers (total in 13 papers)

On the stability and domain of attraction of a stationary nonsmooth limit solution of a singularly perturbed parabolic equation

V. F. Butuzov

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Full-text PDF (1303 kB) Citations (13)
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Abstract: A stationary solution to the singularly perturbed parabolic equation $-u_t+\varepsilon^2u_{xx}-f(u,x)=0$ with Neumann boundary conditions is considered. The limit of the solution as $\varepsilon\to0$ is a nonsmooth solution to the reduced equation $f(u,x)=0$ that is composed of two intersecting roots of this equation. It is proved that the stationary solution is asymptotically stable, and its global domain of attraction is found.
Key words: singularly perturbed parabolic equations, boundary value problem, asymptotic method of solving, stable solutions.
Received: 17.03.2005
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 3, Pages 413–424
DOI: https://doi.org/10.1134/S0965542506030080
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: V. F. Butuzov, “On the stability and domain of attraction of a stationary nonsmooth limit solution of a singularly perturbed parabolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:3 (2006), 433–444; Comput. Math. Math. Phys., 46:3 (2006), 413–424
Citation in format AMSBIB
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\by V.~F.~Butuzov
\paper On the stability and domain of attraction of a~stationary nonsmooth limit solution of a~singularly perturbed parabolic equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 46
\issue 3
\pages 433--444
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\zmath{https://zbmath.org/?q=an:05200915}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 3
\pages 413--424
\crossref{https://doi.org/10.1134/S0965542506030080}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746046700}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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