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Tr. Mat. Inst. Steklova, 1999, Volume 224, Pages 187–207 (Mi tm699)  

This article is cited in 12 scientific papers (total in 13 papers)

Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method

A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov


Abstract: A situation is analyzed when two different curves of slow motion intersect in a general way in a two-dimensional relaxation system. It is shown that this situation gives rise to the so-called duck trajectories. The results of the analysis are applied to the construction of the asymptotics of the principal eigenvalue of the Dirichlet problem for a singularly perturbed Schrödinger equation.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 224, 169–188

Bibliographic databases:
UDC: 517.926
Received in September 1998

Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method”, Algebra. Topology. Differential equations and their applications, Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 224, Nauka, MAIK Nauka/Inteperiodika, M., 1999, 187–207; Proc. Steklov Inst. Math., 224 (1999), 169–188

Citation in format AMSBIB
\Bibitem{KolMisRoz99}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method
\inbook Algebra. Topology. Differential equations and their applications
\bookinfo Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 1999
\vol 224
\pages 187--207
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm699}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1721362}
\zmath{https://zbmath.org/?q=an:0987.34058}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 224
\pages 169--188


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kolesov Y.S., Khar'kov A.E., “Attractors of singularly disturbed reaction–diffusion systems with an extreme turning point in a plane domain”, Doklady Mathematics, 63:2 (2001), 274–276  mathscinet  zmath  isi
    2. A. S. Bobkova, A. Yu. Kolesov, N. Kh. Rozov, “The “Duck Survival” Problem in Three-Dimensional Singularly Perturbed Systems with Two Slow Variables”, Math. Notes, 71:6 (2002), 749–760  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Bobkova A.S., “Duck trajectories in multidimensional singularly perturbed systems with a single fast variable”, Differential Equations, 40:10 (2004), 1373–1382  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Mudavanhu B., O'Malley R.E., Williams D.B., “Working with multiscale asymptotics”, Journal of Engineering Mathematics, 53:3–4 (2005), 301–336  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Xie F., Han M., Zhang W.J., “Canard phenomena in oscillations of a surface oxidation reaction”, Journal of Nonlinear Science, 15:6 (2005), 363–386  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Bobkova A.S., “The behavior of solutions of multidimensional singularly perturbed systems with one fast variable”, Differential Equations, 41:1 (2005), 22–32  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Xie F., Han M.A., Zhang W.J., “The persistence of canards in 3–D singularly perturbed systems with two fast variables”, Asymptotic Analysis, 47:1–2 (2006), 95–106  mathscinet  zmath  isi  elib
    8. Rozov N.Kh., “Duck trajectories of three–dimensional singularly perturbed systems”, Georgian Mathematical Journal, 14:2 (2007), 341–350  mathscinet  zmath  isi
    9. E. S. Golodova, E. A. Shchepakina, “Modelling of safe combustion with maximal temperature”, Math. Models Comput. Simul., 1:2 (2009), 322–334  mathnet  crossref  mathscinet  zmath
    10. Xie F., Han M., “Existence of Canards under Non–generic Conditions”, Chinese Annals of Mathematics Series B, 30:3 (2009), 239–250  crossref  mathscinet  zmath  isi  scopus  scopus
    11. D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. E. S. Golodova, E. A. Schepakina, “Otsenka zatyagivaniya poteri ustoichivosti v differentsialnykh sistemakh s traektoriyami-utkami”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 3(104), 12–24  mathnet
    13. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Many-circuit canard trajectories and their applications”, Izv. Math., 81:4 (2017), 771–817  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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