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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 8, Pages 1356–1364 (Mi zvmmf264)  

This article is cited in 10 scientific papers (total in 10 papers)

On the formation of sharp transition layers in two-dimensional reaction-diffusion models

V. T. Volkov, N. E. Grachëv, N. N. Nefedov, A. N. Nikolaev

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: For a singularly perturbed parabolic equation in two dimensions, the formation of a solution with a sharp transition layer from a sufficiently general initial function is considered. An asymptotic analysis is used to estimate the time required for the formation of a contrast structure. Numerical results are presented.

Key words: two-dimensional reaction-diffusion models, asymptotic solution method, formation of contrast structures in solutions, numerical study.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:8, 1301–1309

Bibliographic databases:

UDC: 519.633.8
Received: 09.01.2007

Citation: V. T. Volkov, N. E. Grachëv, N. N. Nefedov, A. N. Nikolaev, “On the formation of sharp transition layers in two-dimensional reaction-diffusion models”, Zh. Vychisl. Mat. Mat. Fiz., 47:8 (2007), 1356–1364; Comput. Math. Math. Phys., 47:8 (2007), 1301–1309

Citation in format AMSBIB
\by V.~T.~Volkov, N.~E.~Grach\"ev, N.~N.~Nefedov, A.~N.~Nikolaev
\paper On the formation of sharp transition layers in two-dimensional reaction-diffusion models
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 8
\pages 1356--1364
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 8
\pages 1301--1309

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. T. Volkov, N. E. Grachev, A. V. Dmitriev, N. N. Nefedov, “Front formation and dynamics in the reaction-diffusion-advection model”, Math. Models Comput. Simul., 3:2 (2011), 158–164  mathnet  crossref  mathscinet
    2. Yu. V. Bozhevol'nov, N. N. Nefëdov, “Front motion in a parabolic reaction-diffusion problem”, Comput. Math. Math. Phys., 50:2 (2010), 264–273  mathnet  crossref  mathscinet  adsnasa  isi
    3. Grachev N.E., Knyazeva O.S., Kovalenko I.B., “Simulation of phase and component segregation in biological membranes”, Moscow University Physics Bulletin, 65:3 (2010), 227–229  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
    4. Grachev N.E., Dmitriev A.V., Senin D.S., Volkov V.T., Nefedov N.N., “Modelirovanie dinamiki fronta vnutriplastovogo goreniya”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 11:1 (2010), 306–312  mathnet  elib
    5. Volkov V. Nefedov N. Antipov E., “Asymptotic-Numerical Method For Moving Fronts in Two-Dimensional R-D-a Problems”, Finite Difference Methods, Theory and Applications, Lecture Notes in Computer Science, 9045, ed. Dimov I. Farago I. Vulkov L., Springer-Verlag Berlin, 2015, 408–416  crossref  mathscinet  zmath  isi  scopus
    6. D. V. Luk'yanenko, V. T. Volkov, N. N. Nefedov, “Dynamically adapted mesh construction for the efficient numerical solution of a singular perturbed reaction-diffusion-advection equation”, Model. i analiz inform. sistem, 24:3 (2017), 322–338  mathnet  crossref  elib
    7. Volkov V., Lukyanenko D., Nefedov N., “Asymptotic-Numerical Method For the Location and Dynamics of Internal Layers in Singular Perturbed Parabolic Problems”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, eds. Dimov I., Farago I., Vulkov L., Springer International Publishing Ag, 2017, 721–729  crossref  mathscinet  zmath  isi  scopus
    8. Lukyanenko D.V. Shishlenin M.A. Volkov V.T., “Solving of the Coefficient Inverse Problems For a Nonlinear Singularly Perturbed Reaction-Diffusion-Advection Equation With the Final Time Data”, Commun. Nonlinear Sci. Numer. Simul., 54 (2018), 233–247  crossref  mathscinet  isi  scopus
    9. Lukyanenko D.V., Grigorev V.B., Volkov V.T., Shishlenin M.A., “Solving of the Coefficient Inverse Problem For a Nonlinear Singularly Perturbed Two-Dimensional Reaction-Diffusion Equation With the Location of Moving Front Data”, Comput. Math. Appl., 77:5 (2019), 1245–1254  crossref  mathscinet  isi  scopus
    10. Lukyanenko D.V. Volkov V.T. Nefedov N.N. Yagola A.G., “Application of Asymptotic Analysis For Solving the Inverse Problem of Determining the Coefficient of Linear Amplification in Burgers' Equation”, Mosc. Univ. Phys. Bull., 74:2 (2019), 131–136  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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