## Butuzov, Valentin Fëdorovich

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 Author ID: butuzov.valentin-fedorovich Published as: Butuzov, V. F.; Butuzov, Valentin F.; Butuzov, Valentin Fedorovich; Butusov, V. F. External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND
 Documents Indexed: 171 Publications since 1963, including 7 Books 1 Contribution as Editor Biographic References: 2 Publications Co-Authors: 55 Co-Authors with 126 Joint Publications 1,799 Co-Co-Authors
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### Co-Authors

 45 single-authored 25 Nefedov, Nikolaĭ Nikolaevich 21 Vasil’eva, Adelaida Borisovna 14 Nedel’ko, I. V. 13 Schneider, Klaus R. 7 Urazgil’dina, T. A. 6 Nesterov, A. V. 6 Nikitin, Anatoly Glebovich 6 Recke, Lutz 5 Levashova, Natalia T. 4 Buchnev, V. Yu. 4 Kalachev, Leonid V. 4 Kiryushin, V. V. 4 Krutitskaya, N. Ch 4 Mamonov, V. M. 4 Shishkin, A. A. 3 Bychkov, A. I. 3 Derkunova, E. A. 3 Esimova, S. T. 3 Gromova, E. A. 3 Medvedev, G. N. 2 Beloshapko, V. A. 2 Karashchuk, A. F. 2 Kolomijtseva, E. A. 2 Kostin, Andrey Viktorovich 2 Kryazhimskiĭ, S. A. 2 Melnikova, A. A. 2 Moiseev, Evgeniĭ Ivanovich 2 Terent’ev, M. A. 2 Udodov, Yu. P. 1 Aleksandrov, Pavel Sergeevich 1 Alkhutov, Yuriy Alexandrovich 1 Bakhvalov, Nikolai Sergeevich 1 Bogolyubov, Aleksandr Nikolaevich 1 Chechkin, Gregory Aleksandrovich 1 Chubarikov, Vladimir Nikolaevich 1 Fedoryuk, Mikhail V. 1 Fedotova, E. V. 1 Fomin, Sergeĭ Vasil’evich 1 Iliin, V. A. 1 Il’in, Vladimir Aleksandrovich 1 Kon’kov, Andrej A. 1 Kostomarov, Dmitrii Pavlovich 1 Kozlov, Valeriĭ Vasil’evich 1 Mikhalëv, Aleksandr Vasil’evich 1 Omel’chenko, Oleh E. 1 Polezhaeva, E. V. 1 Radkevich, Evgeniĭ Vladimirovich 1 Rozov, Nikolaĭ Khristovich 1 Sadovnichiĭ, Viktor Antonovich 1 Samarskiĭ, Aleksandr Andreevich 1 Sergeev, Igor’ Nikolaevich 1 Shaposhnikova, Tatiana A. 1 Shkalikov, Andreĭ Andreevich 1 Simakov, R. E. 1 Surnachëv, Mikhaĭl Dmitrievich 1 Sushkevich, Tamara A. 1 Tikhomirov, Vladimir Mikhaĭlovich 1 Tikhonov, Andreĭ Nikolaevich 1 Voevodin, Valentin Vasil’evich
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### Serials

 23 Differential Equations 17 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 16 Computational Mathematics and Mathematical Physics 15 Differential Equations 11 Differentsial’nye Uravneniya 10 U.S.S.R. Computational Mathematics and Mathematical Physics 7 Mathematical Notes 6 Moscow University Computational Mathematics and Cybernetics 4 Journal of Mathematical Analysis and Applications 4 Fundamental’naya i Prikladnaya Matematika 4 Doklady Mathematics 4 Matematicheskoe Modelirovanie 3 Journal of Differential Equations 3 Soviet Mathematics. Doklady 3 Journal of Mathematical Sciences (New York) 3 Sbornik: Mathematics 3 Izvestiya: Mathematics 2 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 2 Chebyshevskiĭ Sbornik 1 Applicable Analysis 1 Journal of Applied Mathematics and Mechanics 1 Moscow University Physics Bulletin 1 Russian Mathematical Surveys 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Ukraïns’kyĭ Matematychnyĭ Zhurnal 1 Matematicheskiĭ Sbornik. Novaya Seriya 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Computational Mathematics and Modeling 1 Automation and Remote Control 1 Mathematics of the USSR, Sbornik 1 Vestnik Moskovskogo Universiteta. Seriya 15 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Russian Journal of Mathematical Physics 1 Natural Resource Modeling 1 Proceedings of the Steklov Institute of Mathematics 1 SIAM Studies in Applied Mathematics
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### Fields

 125 Partial differential equations (35-XX) 35 Ordinary differential equations (34-XX) 6 Classical thermodynamics, heat transfer (80-XX) 4 General and overarching topics; collections (00-XX) 4 Integral equations (45-XX) 4 Numerical analysis (65-XX) 4 Fluid mechanics (76-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Difference and functional equations (39-XX) 2 Mechanics of deformable solids (74-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX)

### Citations contained in zbMATH Open

94 Publications have been cited 662 times in 354 Documents Cited by Year
Asymptotic expansion of solutions for singularly perturbed equations. (Асимптотические разложения решений сингулярно возмущенных уравнений.) Zbl 0364.34028
Vasil’eva, A. B.; Butuzov, V. F.
1973
Asymptotic methods in the theory of singular perturbations. (Асимптотические методы в теории сингулярных возмущений.) Zbl 0747.34033
Vasil’eva, A. B.; Butuzov, V. F.
1990
The boundary function method for singular perturbation problems. Zbl 0823.34059
Vasil’eva, Adelaida B.; Butuzov, Valentin F.; Kalachev, Leonid V.
1995
Singularly perturbed problems with boundary and internal layers. Zbl 1207.35039
Vasil’eva, A. B.; Butuzov, V. F.; Nefedov, N. N.
2010
Contrast structures in singularly perturbed problems. Zbl 0963.34043
Vasil’eva, A. B.; Butuzov, V. F.; Nefedov, N. N.
1998
Singularly perturbed elliptic problems in the case of exchange of stabilities. Zbl 0974.35039
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2001
On the special properties of the boundary layer in singularly perturbed problems with multiple root of the degenerate equation. Zbl 1284.34099
Butuzov, V. F.
2013
Asymptotic theory of contrast structures (review). Zbl 0921.34054
Butuzov, V. F.; Vasil’eva, A. B.; Nefedov, N. N.
1997
Singularly perturbed problems in case of exchange of stabilities. Zbl 1081.34051
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2004
On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation. Zbl 1224.35225
Butuzov, V. F.
2011
Steplike contrast structure in a singularly perturbed system of equations with different powers of a small parameter. Zbl 1274.35014
Butuzov, V. F.; Levashova, N. T.; Mel’nikova, A. A.
2012
Asymptotics of the solution to an initial boundary value problem for a singularly perturbed parabolic equation in the case of a triple root of the degenerate equation. Zbl 1350.35013
Butuzov, V. F.; Bychkov, A. I.
2016
Asymptotics of the solution of an initial-boundary value problem for a singularly perturbed parabolic equation in the case of double root of the degenerate equation. Zbl 1295.35032
Butuzov, V. F.; Bychkov, A. I.
2013
On a singularly perturbed initial value problem in the case of a double root of the degenerate equation. Zbl 1268.34104
Butuzov, V. F.; Nefedov, N. N.; Recke, L.; Schneider, K. R.
2013
On the stability and the attraction domain of the stationary solution of a singularly perturbed parabolic equation with a multiple root of the degenerate equation. Zbl 06567311
Butuzov, V. F.
2015
Time-periodic boundary layer solutions to singularly perturbed parabolic problems. Zbl 1362.35031
Omel’chenko, O. E.; Recke, L.; Butuzov, V. F.; Nefedov, N. N.
2017
Singularly perturbed boundary value problems in case of exchange of stability. Zbl 0924.34014
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
1999
The asymptotic properties of solutions of the equation $$\mu^2\Delta u- k^2(x,y)u=f(x,y)$$ in a rectangle. Zbl 0306.35037
Butuzov, V. F.
1975
Asymptotic properties of the solution of a finite-difference equation with small steps in a rectangular region. Zbl 0278.65103
Butuzov, V. F.
1973
Asymptotic behaviour and stability of solutions of a singularly perturbed elliptic problem with a triple root of the degenerate equation. Zbl 1373.35026
Butuzov, Valentin F.
2017
Singularly perturbed boundary value problems for systems of Tichonov’s type in case of exchange of stabilities. Zbl 0944.34048
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
1999
A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability. Zbl 0920.34023
Butuzov, V. F.; Nefedov, N. N.
1998
Initial boundary value problem for a singularly perturbed parabolic equation in case of exchange of stability. Zbl 1005.35055
Butuzov, V. F.; Smurov, I.
1999
On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic equation. Zbl 1210.35147
Butuzov, V. F.
2006
Spikelike contrast structures in the parabolic system of two singularly perturbed equations. Zbl 0940.35023
Butuzov, V. F.
1997
Periodic solutions with a boundary layer of reaction-diffusion equations with singularly perturbed Neumann boundary conditions. Zbl 1300.35002
Butuzov, Valentin F.; Nefedov, Nikolay N.; Recke, Lutz; Schneider, Klaus R.
2014
Asymptotic approximation of solution of boundary-value problem for a singularly perturbed parabolic equation in the critical case. Zbl 0628.35049
Butuzov, V. F.; Kalachëv, L. V.
1986
Asymptotisches Verhalten der Lösung der Gleichung $$\mu ^2 \Delta u - k^2 (x,y) u=f(x,y)$$ in einem rechteckigen Gebiet. Zbl 0271.35016
Butuzov, V. F.
1973
A singularly perturbed elliptic equation with two small parameters. Zbl 0366.35008
Butuzov, V. F.
1977
Asymptotics of the solution of a system of singularly perturbed equations in the case of a multiple root of the degenerate equation. Zbl 1367.34081
Butuzov, V. F.
2014
A step-like contrast structure in a singularly perturbed system of elliptic equations. Zbl 1299.35027
Butuzov, V. F.; Levashova, N. T.; Mel’nikova, A. A.
2013
Region of attraction of a periodic solution to a singularly perturbed parabolic problem. Zbl 1253.35011
Butuzov, V. F.; Nefedov, N. N.; Recke, L.; Schneider, K. R.
2012
Differential and difference equation systems with a small parameter for the case in which the unperturbed (singular) system is in the spectrum. Zbl 0249.65056
Butuzov, V. F.; Vasil’eva, A. B.
1973
Mathematical analysis in questions and answers. (Matematicheskij analiz v voprosakh i zadachakh). 3rd rev. ed. (Matematicheskij analiz v voprosakh i zadachakh.) Zbl 1029.00002
Butuzov, V. F.; Krutitskaya, N. Ch.; Medvedev, G. N.; Shishkin, A. A.
2000
Asymptotic of a solution of contrast-structure type. Zbl 0725.34061
Butuzov, V. F.; Vasil’eva, A. B.
1987
Asymptotics of a solution of a singularly perturbed parabolic problem in the two-dimensional case. Zbl 0688.35031
Butuzov, V. F.; Buchnev, V. Yu.
1989
Die Winkelgrenzschicht in singulär gestörten Problemen mit partiellen Ableitungen. Zbl 0423.35025
Butuzov, V. F.
1979
On the dependence of the structure of boundary layers on the boundary conditions in a singularly perturbed boundary-value problem with multiple root of the related degenerate equation. Zbl 1347.34093
Butuzov, V. F.
2016
Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation. Zbl 1361.35085
Butuzov, Valentin F.
2016
On a system of reaction-diffusion-transfer type in the case of small diffusion and fast reactions. Zbl 1136.35408
Butuzov, V. F.; Levashova, N. T.
2003
Asymptotics of solutions to a boundary value problem for the heat equation with a powerful nonlinear source in a thin rod. Zbl 0856.35053
Butuzov, V. F.; Urazgil’dina, T. A.
1995
On a singularly perturbed reaction-diffusion-transfer system in the case of slow diffusion and fast reactions. Zbl 0867.35007
Butuzov, V. F.; Levashova, N. T.
1995
Singularly perturbed reaction-diffusion systems in cases of exchange of stabilities. Zbl 0980.35023
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2000
On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer. Zbl 1397.35011
Butuzov, V. F.
2018
On some singularly perturbed problems with nonsmooth boundary functions. Zbl 0508.35012
Butuzov, V. F.; Nesterov, A. V.
1982
The asymptotic behaviour of the solution of a singularly perturbed two- dimensional problem of the reaction-diffusion-transport type. Zbl 0779.35015
Butuzov, V. F.; Buchnev, V. Yu.
1991
Asymptotic solution of the linearized problem of the propagation of sound in a bounded medium with low viscosity. Zbl 0659.76092
Butuzov, V. F.; Nefëdov, N. N.; Fedotova, E. V.
1987
Asymptotic approximation of the solution of a singularly perturbed parabolic two-dimensional problem with a nonsmooth limit solution. Zbl 0714.35007
Butuzov, V. F.; Buchnev, V. Yu.
1989
Existence and stability of solutions with periodically moving weak internal layers. Zbl 1158.35010
Butuzov, V. F.; Nefedov, N. N.; Recke, L.; Schneider, K. R.
2008
The asymptotics of solutions of some model problems in chemical kinetics, taking diffusion into account. Zbl 0416.35010
Butuzov, V. F.
1978
Asymptotic behavior and stability of a stationary boundary-layer solution to a partially dissipative system of equations. Zbl 1430.35014
Butuzov, V. F.
2019
A problem in singular-perturbation theory. Zbl 0375.34035
Butuzov, V. F.; Nefedov, N. N.
1977
A singularly perturbed elliptic problem in the case of a multiple root of the degenerate equation. Zbl 1299.35026
Beloshapko, V. A.; Butuzov, V. F.
2013
A steplike contrast structure in a singularly perturbed system of elliptic equations with different power of a small parameter. Zbl 0993.35036
Butuzov, V. F.; Nedel’ko, I. V.
2000
Singularly perturbed partly dissipative reaction-diffusion systems in case of exchange of stabilities. Zbl 1192.35096
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2002
Boundary value problem for a system of fast and slow second-order equations in the case of intersecting roots of the degenerate equation. Zbl 1036.34061
Butuzov, V. F.; Gromova, E. A.
2001
Asymptotic methods in the theory of ordinary differential equations. Zbl 0246.34055
Butuzov, V. F.; Vasil’eva, A. B.; Fedoryuk, M. V.
1970
One singularly perturbed equation of parabolic type. Zbl 0445.35014
Butuzov, V. F.; Nesterov, A. V.
1978
Singularly perturbed differential equations of parabolic type. Zbl 0506.35010
Butuzov, V. F.; Vasil’eva, A. B.
1983
Asymptotisches Verhalten der Lösung einer Integrodifferentialgleichung mit einem kleinem Parameter der Abteilung. Zbl 0184.14402
Vasil’eva, A. B.; Butuzov, V. F.
1964
Existence and asymptotic stability of a stationary solution of a singularly perturbed system of parabolic equations in the case of intersecting roots of the degenerate equation. Zbl 1279.34067
Butuzov, V. F.
2006
On singularly perturbed systems of ODE with a multiple root of the degenerate equation. Zbl 1445.34087
Butuzov, Valentin F.
2020
Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation. Zbl 1480.34077
Butuzov, V. F.
2019
Asymptotic properties of solutions of singularly perturbed elliptic equations in rectangular regions. Zbl 0334.35007
Butuzov, V. F.
1976
Asymptotic expansion of the solution to a partially dissipative system of equations with a multizone boundary layer. Zbl 1443.34054
Butuzov, V. F.
2019
Corner boundary layers in singularly perturbed problems for partial differential equations. Zbl 0437.35012
Butuzov, V. F.
1980
System of singularly perturbed equations in the case of intersecting roots of a degenerate system. Zbl 1079.34530
Butuzov, V. F.; Terent’ev, M. A.
2002
Asymptotic behavior of the solution of a singularly perturbed system of reaction-diffusion equations in a thin rod. Zbl 1136.35402
Butuzov, V. F.; Levashova, N. T.
2003
Global influence domains of stable solutions with internal layers. Zbl 1009.35008
Butuzov, V. F.; Nedel’ko, I. V.
2001
Spatially periodic contrast structures in singularly perturbed elliptic problems. Zbl 0897.35007
Butuzov, V. F.; Nefedov, N. N.
1996
Asymptotic behavior of the solution of the heat equation with a nonlinear heat source in a thin rod. Zbl 1161.35430
Butuzov, V. F.; Derkunova, E. A.
1996
Asymptotics of a Spike type contrast structure in a problem with a multiple root of the degenerate equation. Zbl 1460.34070
Butuzov, V. F.
2019
Asymptotics of the solution of non-stationary interphase convection problem in thin layer of viscous fluid. Zbl 1075.76680
Butuzov, V. F.; Urazgil’dina, T. A.
1994
Singularly perturbed elliptic boundary-value problems in the critical case. Zbl 0564.35003
Butuzov, V. F.; Mamonov, V. M.
1982
On the global domain of influence of stable solutions with interior layers in the two-dimensional case. Zbl 1091.35037
Butuzov, V. F.; Nedel’ko, I. V.
2002
Asymptotic solution of a system of singularly disturbed equations of elliptic type with angular boundary layer. Zbl 0468.35012
Butuzov, V. F.; Udodov, Yu. P.
1981
On the asymptotic behavior of the solution of an equation of parabolic type with small parameters at the higher derivatives. Zbl 0513.35038
Butuzov, V. F.; Nesterov, A. V.
1982
Über eine Integrodifferentialgleichung mit einem kleinen Parameter bei der Ableitung für den Fall, daß sich die entartete Gleichung auf dem Spektrum befindet. Zbl 0216.40501
Butuzov, V. F.
1971
The angular boundary layer in mixed singularly perturbed problems for hyperbolic equations. Zbl 0398.35005
Butuzov, V. F.
1977
Asymptotic solution of the heat propagation problem in thin bodies. Zbl 0621.35056
Butuzov, V. F.; Urazgil’dina, T. A.
1987
Some singularly perturbed hyperbolic problems with transitional layers. Zbl 0625.35052
Butuzov, V. F.; Nesterov, A. V.
1986
The boundary-function method. Zbl 0644.35008
Vasil’eva, A. B.; Butuzov, V. F.
1985
Asymptotic solution of the problem concerning the propagation of heat in thin bodies. Zbl 0662.35064
Butuzov, V. F.; Urazgil’dina, T. A.
1987
Asymptotic solution of a quasistatic thermoelaticity problem for a slender rod. Zbl 0677.73011
Butuzov, V. F.; Urazgil’dina, T. A.
1987
The asymptotic theory of contrasting spatial structures. Zbl 0702.35124
Butuzov, V. F.; Vasil’eva, A. B.
1988
On a singularly perturbed quasilinear parabolic problem with unsmooth corner boundary functions. Zbl 0711.35009
Butuzov, V. F.; Mamonov, V. M.
1987
Singularly perturbed systems of reaction-diffusion-transport type. Zbl 0838.35007
Butuzov, V. F.
1993
Singularly disturbed elliptic boundary value problem in a rectangle in the critical case. Zbl 0589.35039
Butuzov, V. F.; Nikitin, A. G.
1984
Boundary layer methods in singularly perturbed partial differential equations. Zbl 0674.35003
Vasil’eva, A. B.; Butuzov, V. F.
1986
On one singularly perturbed system of ordinary differential equations with multiple root of the degenerate equation. Zbl 1440.34059
Butuzov, V. F.
2019
Asymptotics of the solution to a singularly perturbed elliptic problem with a three-zone boundary layer. Zbl 1362.35029
Beloshapko, V. A.; Butuzov, V. F.
2016
Eine singulär gestörte Gleichung elliptischen Typs mit zwei kleinen Parametern. Zbl 0341.35006
Butuzov, V. F.
1976
Winkelgrenzschicht in gemischten singulär gestörten Problemen für hyperbolische Gleichungen. Zbl 0367.35007
Butuzov, V. F.
1977
Asymptotics of a steplike contrast structure in a partially dissipative stationary system of equations. Zbl 1466.34054
Butuzov, V. F.
2021
Asymptotics of a steplike contrast structure in a partially dissipative stationary system of equations. Zbl 1466.34054
Butuzov, V. F.
2021
On singularly perturbed systems of ODE with a multiple root of the degenerate equation. Zbl 1445.34087
Butuzov, Valentin F.
2020
Asymptotic behavior and stability of a stationary boundary-layer solution to a partially dissipative system of equations. Zbl 1430.35014
Butuzov, V. F.
2019
Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation. Zbl 1480.34077
Butuzov, V. F.
2019
Asymptotic expansion of the solution to a partially dissipative system of equations with a multizone boundary layer. Zbl 1443.34054
Butuzov, V. F.
2019
Asymptotics of a Spike type contrast structure in a problem with a multiple root of the degenerate equation. Zbl 1460.34070
Butuzov, V. F.
2019
On one singularly perturbed system of ordinary differential equations with multiple root of the degenerate equation. Zbl 1440.34059
Butuzov, V. F.
2019
On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer. Zbl 1397.35011
Butuzov, V. F.
2018
Time-periodic boundary layer solutions to singularly perturbed parabolic problems. Zbl 1362.35031
Omel&rsquo;chenko, O. E.; Recke, L.; Butuzov, V. F.; Nefedov, N. N.
2017
Asymptotic behaviour and stability of solutions of a singularly perturbed elliptic problem with a triple root of the degenerate equation. Zbl 1373.35026
Butuzov, Valentin F.
2017
Asymptotics of the solution to an initial boundary value problem for a singularly perturbed parabolic equation in the case of a triple root of the degenerate equation. Zbl 1350.35013
Butuzov, V. F.; Bychkov, A. I.
2016
On the dependence of the structure of boundary layers on the boundary conditions in a singularly perturbed boundary-value problem with multiple root of the related degenerate equation. Zbl 1347.34093
Butuzov, V. F.
2016
Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation. Zbl 1361.35085
Butuzov, Valentin F.
2016
Asymptotics of the solution to a singularly perturbed elliptic problem with a three-zone boundary layer. Zbl 1362.35029
Beloshapko, V. A.; Butuzov, V. F.
2016
On the stability and the attraction domain of the stationary solution of a singularly perturbed parabolic equation with a multiple root of the degenerate equation. Zbl 06567311
Butuzov, V. F.
2015
Periodic solutions with a boundary layer of reaction-diffusion equations with singularly perturbed Neumann boundary conditions. Zbl 1300.35002
Butuzov, Valentin F.; Nefedov, Nikolay N.; Recke, Lutz; Schneider, Klaus R.
2014
Asymptotics of the solution of a system of singularly perturbed equations in the case of a multiple root of the degenerate equation. Zbl 1367.34081
Butuzov, V. F.
2014
On the special properties of the boundary layer in singularly perturbed problems with multiple root of the degenerate equation. Zbl 1284.34099
Butuzov, V. F.
2013
Asymptotics of the solution of an initial-boundary value problem for a singularly perturbed parabolic equation in the case of double root of the degenerate equation. Zbl 1295.35032
Butuzov, V. F.; Bychkov, A. I.
2013
On a singularly perturbed initial value problem in the case of a double root of the degenerate equation. Zbl 1268.34104
Butuzov, V. F.; Nefedov, N. N.; Recke, L.; Schneider, K. R.
2013
A step-like contrast structure in a singularly perturbed system of elliptic equations. Zbl 1299.35027
Butuzov, V. F.; Levashova, N. T.; Mel&rsquo;nikova, A. A.
2013
A singularly perturbed elliptic problem in the case of a multiple root of the degenerate equation. Zbl 1299.35026
Beloshapko, V. A.; Butuzov, V. F.
2013
Steplike contrast structure in a singularly perturbed system of equations with different powers of a small parameter. Zbl 1274.35014
Butuzov, V. F.; Levashova, N. T.; Mel&rsquo;nikova, A. A.
2012
Region of attraction of a periodic solution to a singularly perturbed parabolic problem. Zbl 1253.35011
Butuzov, V. F.; Nefedov, N. N.; Recke, L.; Schneider, K. R.
2012
On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation. Zbl 1224.35225
Butuzov, V. F.
2011
Singularly perturbed problems with boundary and internal layers. Zbl 1207.35039
Vasil&rsquo;eva, A. B.; Butuzov, V. F.; Nefedov, N. N.
2010
Existence and stability of solutions with periodically moving weak internal layers. Zbl 1158.35010
Butuzov, V. F.; Nefedov, N. N.; Recke, L.; Schneider, K. R.
2008
On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic equation. Zbl 1210.35147
Butuzov, V. F.
2006
Existence and asymptotic stability of a stationary solution of a singularly perturbed system of parabolic equations in the case of intersecting roots of the degenerate equation. Zbl 1279.34067
Butuzov, V. F.
2006
Singularly perturbed problems in case of exchange of stabilities. Zbl 1081.34051
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2004
On a system of reaction-diffusion-transfer type in the case of small diffusion and fast reactions. Zbl 1136.35408
Butuzov, V. F.; Levashova, N. T.
2003
Asymptotic behavior of the solution of a singularly perturbed system of reaction-diffusion equations in a thin rod. Zbl 1136.35402
Butuzov, V. F.; Levashova, N. T.
2003
Singularly perturbed partly dissipative reaction-diffusion systems in case of exchange of stabilities. Zbl 1192.35096
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2002
System of singularly perturbed equations in the case of intersecting roots of a degenerate system. Zbl 1079.34530
Butuzov, V. F.; Terent&rsquo;ev, M. A.
2002
On the global domain of influence of stable solutions with interior layers in the two-dimensional case. Zbl 1091.35037
Butuzov, V. F.; Nedel&rsquo;ko, I. V.
2002
Singularly perturbed elliptic problems in the case of exchange of stabilities. Zbl 0974.35039
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2001
Boundary value problem for a system of fast and slow second-order equations in the case of intersecting roots of the degenerate equation. Zbl 1036.34061
Butuzov, V. F.; Gromova, E. A.
2001
Global influence domains of stable solutions with internal layers. Zbl 1009.35008
Butuzov, V. F.; Nedel&rsquo;ko, I. V.
2001
Mathematical analysis in questions and answers. (Matematicheskij analiz v voprosakh i zadachakh). 3rd rev. ed. (Matematicheskij analiz v voprosakh i zadachakh.) Zbl 1029.00002
Butuzov, V. F.; Krutitskaya, N. Ch.; Medvedev, G. N.; Shishkin, A. A.
2000
Singularly perturbed reaction-diffusion systems in cases of exchange of stabilities. Zbl 0980.35023
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2000
A steplike contrast structure in a singularly perturbed system of elliptic equations with different power of a small parameter. Zbl 0993.35036
Butuzov, V. F.; Nedel&rsquo;ko, I. V.
2000
Singularly perturbed boundary value problems in case of exchange of stability. Zbl 0924.34014
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
1999
Singularly perturbed boundary value problems for systems of Tichonov’s type in case of exchange of stabilities. Zbl 0944.34048
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
1999
Initial boundary value problem for a singularly perturbed parabolic equation in case of exchange of stability. Zbl 1005.35055
Butuzov, V. F.; Smurov, I.
1999
Contrast structures in singularly perturbed problems. Zbl 0963.34043
Vasil&rsquo;eva, A. B.; Butuzov, V. F.; Nefedov, N. N.
1998
A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability. Zbl 0920.34023
Butuzov, V. F.; Nefedov, N. N.
1998
Asymptotic theory of contrast structures (review). Zbl 0921.34054
Butuzov, V. F.; Vasil&rsquo;eva, A. B.; Nefedov, N. N.
1997
Spikelike contrast structures in the parabolic system of two singularly perturbed equations. Zbl 0940.35023
Butuzov, V. F.
1997
Spatially periodic contrast structures in singularly perturbed elliptic problems. Zbl 0897.35007
Butuzov, V. F.; Nefedov, N. N.
1996
Asymptotic behavior of the solution of the heat equation with a nonlinear heat source in a thin rod. Zbl 1161.35430
Butuzov, V. F.; Derkunova, E. A.
1996
The boundary function method for singular perturbation problems. Zbl 0823.34059
Vasil&rsquo;eva, Adelaida B.; Butuzov, Valentin F.; Kalachev, Leonid V.
1995
Asymptotics of solutions to a boundary value problem for the heat equation with a powerful nonlinear source in a thin rod. Zbl 0856.35053
Butuzov, V. F.; Urazgil&rsquo;dina, T. A.
1995
On a singularly perturbed reaction-diffusion-transfer system in the case of slow diffusion and fast reactions. Zbl 0867.35007
Butuzov, V. F.; Levashova, N. T.
1995
Asymptotics of the solution of non-stationary interphase convection problem in thin layer of viscous fluid. Zbl 1075.76680
Butuzov, V. F.; Urazgil&rsquo;dina, T. A.
1994
Singularly perturbed systems of reaction-diffusion-transport type. Zbl 0838.35007
Butuzov, V. F.
1993
The asymptotic behaviour of the solution of a singularly perturbed two- dimensional problem of the reaction-diffusion-transport type. Zbl 0779.35015
Butuzov, V. F.; Buchnev, V. Yu.
1991
Asymptotic methods in the theory of singular perturbations. (Асимптотические методы в теории сингулярных возмущений.) Zbl 0747.34033
Vasil&rsquo;eva, A. B.; Butuzov, V. F.
1990
Asymptotics of a solution of a singularly perturbed parabolic problem in the two-dimensional case. Zbl 0688.35031
Butuzov, V. F.; Buchnev, V. Yu.
1989
Asymptotic approximation of the solution of a singularly perturbed parabolic two-dimensional problem with a nonsmooth limit solution. Zbl 0714.35007
Butuzov, V. F.; Buchnev, V. Yu.
1989
The asymptotic theory of contrasting spatial structures. Zbl 0702.35124
Butuzov, V. F.; Vasil&rsquo;eva, A. B.
1988
Asymptotic of a solution of contrast-structure type. Zbl 0725.34061
Butuzov, V. F.; Vasil&rsquo;eva, A. B.
1987
Asymptotic solution of the linearized problem of the propagation of sound in a bounded medium with low viscosity. Zbl 0659.76092
Butuzov, V. F.; Nefëdov, N. N.; Fedotova, E. V.
1987
Asymptotic solution of the heat propagation problem in thin bodies. Zbl 0621.35056
Butuzov, V. F.; Urazgil&rsquo;dina, T. A.
1987
Asymptotic solution of the problem concerning the propagation of heat in thin bodies. Zbl 0662.35064
Butuzov, V. F.; Urazgil&rsquo;dina, T. A.
1987
Asymptotic solution of a quasistatic thermoelaticity problem for a slender rod. Zbl 0677.73011
Butuzov, V. F.; Urazgil&rsquo;dina, T. A.
1987
On a singularly perturbed quasilinear parabolic problem with unsmooth corner boundary functions. Zbl 0711.35009
Butuzov, V. F.; Mamonov, V. M.
1987
Asymptotic approximation of solution of boundary-value problem for a singularly perturbed parabolic equation in the critical case. Zbl 0628.35049
Butuzov, V. F.; Kalachëv, L. V.
1986
Some singularly perturbed hyperbolic problems with transitional layers. Zbl 0625.35052
Butuzov, V. F.; Nesterov, A. V.
1986
Boundary layer methods in singularly perturbed partial differential equations. Zbl 0674.35003
Vasil&rsquo;eva, A. B.; Butuzov, V. F.
1986
The boundary-function method. Zbl 0644.35008
Vasil&rsquo;eva, A. B.; Butuzov, V. F.
1985
Singularly disturbed elliptic boundary value problem in a rectangle in the critical case. Zbl 0589.35039
Butuzov, V. F.; Nikitin, A. G.
1984
Singularly perturbed differential equations of parabolic type. Zbl 0506.35010
Butuzov, V. F.; Vasil&rsquo;eva, A. B.
1983
On some singularly perturbed problems with nonsmooth boundary functions. Zbl 0508.35012
Butuzov, V. F.; Nesterov, A. V.
1982
Singularly perturbed elliptic boundary-value problems in the critical case. Zbl 0564.35003
Butuzov, V. F.; Mamonov, V. M.
1982
On the asymptotic behavior of the solution of an equation of parabolic type with small parameters at the higher derivatives. Zbl 0513.35038
Butuzov, V. F.; Nesterov, A. V.
1982
Asymptotic solution of a system of singularly disturbed equations of elliptic type with angular boundary layer. Zbl 0468.35012
Butuzov, V. F.; Udodov, Yu. P.
1981
Corner boundary layers in singularly perturbed problems for partial differential equations. Zbl 0437.35012
Butuzov, V. F.
1980
Die Winkelgrenzschicht in singulär gestörten Problemen mit partiellen Ableitungen. Zbl 0423.35025
Butuzov, V. F.
1979
The asymptotics of solutions of some model problems in chemical kinetics, taking diffusion into account. Zbl 0416.35010
Butuzov, V. F.
1978
One singularly perturbed equation of parabolic type. Zbl 0445.35014
Butuzov, V. F.; Nesterov, A. V.
1978
A singularly perturbed elliptic equation with two small parameters. Zbl 0366.35008
Butuzov, V. F.
1977
A problem in singular-perturbation theory. Zbl 0375.34035
Butuzov, V. F.; Nefedov, N. N.
1977
The angular boundary layer in mixed singularly perturbed problems for hyperbolic equations. Zbl 0398.35005
Butuzov, V. F.
1977
Winkelgrenzschicht in gemischten singulär gestörten Problemen für hyperbolische Gleichungen. Zbl 0367.35007
Butuzov, V. F.
1977
Asymptotic properties of solutions of singularly perturbed elliptic equations in rectangular regions. Zbl 0334.35007
Butuzov, V. F.
1976
Eine singulär gestörte Gleichung elliptischen Typs mit zwei kleinen Parametern. Zbl 0341.35006
Butuzov, V. F.
1976
The asymptotic properties of solutions of the equation $$\mu^2\Delta u- k^2(x,y)u=f(x,y)$$ in a rectangle. Zbl 0306.35037
Butuzov, V. F.
1975
Asymptotic expansion of solutions for singularly perturbed equations. (Асимптотические разложения решений сингулярно возмущенных уравнений.) Zbl 0364.34028
Vasil&rsquo;eva, A. B.; Butuzov, V. F.
1973
Asymptotic properties of the solution of a finite-difference equation with small steps in a rectangular region. Zbl 0278.65103
Butuzov, V. F.
1973
Asymptotisches Verhalten der Lösung der Gleichung $$\mu ^2 \Delta u - k^2 (x,y) u=f(x,y)$$ in einem rechteckigen Gebiet. Zbl 0271.35016
Butuzov, V. F.
1973
Differential and difference equation systems with a small parameter for the case in which the unperturbed (singular) system is in the spectrum. Zbl 0249.65056
Butuzov, V. F.; Vasil&rsquo;eva, A. B.
1973
Über eine Integrodifferentialgleichung mit einem kleinen Parameter bei der Ableitung für den Fall, daß sich die entartete Gleichung auf dem Spektrum befindet. Zbl 0216.40501
Butuzov, V. F.
1971
Asymptotic methods in the theory of ordinary differential equations. Zbl 0246.34055
Butuzov, V. F.; Vasil&rsquo;eva, A. B.; Fedoryuk, M. V.
1970
Asymptotisches Verhalten der Lösung einer Integrodifferentialgleichung mit einem kleinem Parameter der Abteilung. Zbl 0184.14402
Vasil&rsquo;eva, A. B.; Butuzov, V. F.
1964
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### Cited by 331 Authors

 42 Nefedov, Nikolaĭ Nikolaevich 41 Butuzov, Valentin Fëdorovich 20 Ni, Mingkang 18 Levashova, Natalia T. 14 Mo, Jiaqi 14 Schneider, Klaus R. 10 Davydova, M. A. 10 Kashchenko, Sergeĭ Aleksandrovich 9 Nikulin, E. I. 9 Recke, Lutz 6 Denisov, Igor’ Vasil’evich 6 Kachalov, Vasily Ivanovich 6 Kopteva, Natalia Viktorovna 6 Li, Jichun 6 Luk’yanenko, Dmitriĭ Vital’evich 6 Sobolev, Vladimir A. 5 Dmitriev, M. G. 5 Glizer, Valery Y. 5 Kalachev, Leonid V. 5 Lin, Wantao 5 Melnikova, A. A. 5 Orlov, Andrey O. 5 Sourdis, Christos 4 Bukzhalëv, Evgeniĭ Evgen’evich 4 Hoai, Nguyen Thi Xuan 4 Krutitskii, Pavel A. 4 Kurina, Galina A. 4 Navon, Ionel Michael 4 Nikolaeva, Olga A. 4 Omuraliev, Asan S. 4 Shishlenin, Maxim Aleksandrovich 4 Vasil’eva, Adelaida Borisovna 4 Vlakhova, A. V. 4 Zakharova, S. A. 3 Banasiak, Jacek 3 Belolipetskij, A. A. 3 Bobodzhanov, Abdukhafiz Abdurasulovich 3 Braianov, Ilia A. 3 Bychkov, A. I. 3 Bykov, Aleksei Aleksandrovich 3 Kalimbetov, Burkhan T. 3 Kalinin, Anatoly I. 3 Karali, Georgia D. 3 Korobeinikov, Andrei 3 Reznichenko, I. O. 3 Roos, Hans-Görg 3 Safonov, Valeriĭ Fedorovich 3 Stynes, Martin 3 Su, Yucheng 3 Ter-Krikorov, A. M. 3 Volkov, Vladimir T. 3 Wang, Zhiming 3 Wu, Limeng 2 Archibasov, A. A. 2 Beloshapko, V. A. 2 Blatov, Igor A. 2 Bobryk, Roman V. 2 Chaturvedi, Abhay Kumar 2 Denisov, A. I. 2 Derkunova, E. A. 2 Dzhumabaev, Dulat Syzdykbekovich 2 Ermakova, Kristina Evgenievna 2 Filippychev, D. S. 2 Kadalbajoo, Mohan K. 2 Kellogg, Bruce 2 Kolybasova, V. V. 2 Kuzmina, Lyudmila K. 2 Lavrinovich, L. I. 2 López, José Luis 2 Lu, Haibo 2 Mika, Janusz R. 2 Mingkang, Ni 2 Nazarov, Sergeĭ Aleksandrovich 2 Novoderova, A. P. 2 O’Malley, Robert E. jun. 2 Orozov, M. O. 2 Patidar, Kailash C. 2 Pérez Sinusía, Ester 2 Qi, Xutian 2 Rachinskii, Dmitrii I. 2 Rao, S. Chandra Sekhara 2 Samoĭlenko, Anatoliĭ Mykhaĭlovych 2 Samusenko, Petro F. 2 Seidman, Thomas I. 2 Sinitsyn, E. V. 2 Strygin, Vadim V. 2 Tchamga, Milaine Sergine Seuneu 2 Teofanov, Ljiljana 2 Tursunov, Dilmurat Abdillazhanovich 2 Urazgil’dina, T. A. 2 Uskov, Vladimir Igorevich 2 Wang, Aifeng 2 Wang, Hui 2 Wu, Xiao 2 Wyller, John A. 2 Yagremtsev, A. V. 2 Yang, Qian 2 Zhu, Jiang 2 Zubova, Svetlana Petrovna 1 Abood, H. D. ...and 231 more Authors
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### Cited in 93 Serials

 41 Computational Mathematics and Mathematical Physics 39 Differential Equations 26 Journal of Mathematical Analysis and Applications 23 Journal of Applied Mathematics and Mechanics 16 Mathematical Notes 10 Applied Mathematics and Computation 10 Journal of Mathematical Sciences (New York) 9 Computers & Mathematics with Applications 8 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 7 Ukrainian Mathematical Journal 7 Applied Mathematics. Series B (English Edition) 6 Russian Journal of Mathematical Physics 5 Journal of Computational and Applied Mathematics 5 Journal of Differential Equations 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Applied Mathematics and Mechanics. (English Edition) 4 Theoretical and Mathematical Physics 4 Doklady Mathematics 4 Lobachevskii Journal of Mathematics 4 Proceedings of the Steklov Institute of Mathematics 3 Computer Methods in Applied Mechanics and Engineering 3 Applied Numerical Mathematics 3 Sbornik: Mathematics 3 Abstract and Applied Analysis 3 Communications in Nonlinear Science and Numerical Simulation 3 Qualitative Theory of Dynamical Systems 3 Nonlinear Analysis. Real World Applications 3 Boundary Value Problems 2 Applicable Analysis 2 Moscow University Mathematics Bulletin 2 Moscow University Mechanics Bulletin 2 Mathematics of Computation 2 Prikladnaya Matematika i Mekhanika 2 Automatica 2 Journal of Optimization Theory and Applications 2 Siberian Mathematical Journal 2 Transactions of the Moscow Mathematical Society 2 Moscow University Computational Mathematics and Cybernetics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Computational Mathematics and Modeling 2 Automation and Remote Control 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Journal of Dynamics and Differential Equations 2 Izvestiya: Mathematics 2 Discrete Dynamics in Nature and Society 2 Journal of Dynamical and Control Systems 2 Journal of Zhejiang University. Science 2 Matematicheskoe Modelirovanie 2 Science China. Mathematics 2 Open Mathematics 2 1 Archive for Rational Mechanics and Analysis 1 Journal of the Franklin Institute 1 Rocky Mountain Journal of Mathematics 1 Numerische Mathematik 1 Proceedings of the Japan Academy. Series A 1 Systems & Control Letters 1 Zeitschrift für Analysis und ihre Anwendungen 1 Circuits, Systems, and Signal Processing 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Mathematical and Computer Modelling 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Communications in Partial Differential Equations 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Russian Mathematics 1 Theory of Probability and Mathematical Statistics 1 Computational and Applied Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 Discrete and Continuous Dynamical Systems 1 Nonlinear Dynamics 1 Vietnam Journal of Mathematics 1 Journal of Applied Mechanics and Technical Physics 1 Journal of Shanghai University 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 European Journal of Mechanics. B. Fluids 1 Natural Resource Modeling 1 Regular and Chaotic Dynamics 1 Journal of Evolution Equations 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Analysis in Theory and Applications 1 International Journal of Numerical Analysis and Modeling 1 Mathematical Biosciences and Engineering 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Chebyshevskiĭ Sbornik 1 Discrete and Continuous Dynamical Systems. Series S 1 Analysis and Mathematical Physics 1 Journal of Applied Analysis and Computation 1 Axioms 1 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematika. Mekhanika. Fizika 1 AIMS Mathematics 1 SN Partial Differential Equations and Applications
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### Cited in 23 Fields

 167 Partial differential equations (35-XX) 141 Ordinary differential equations (34-XX) 54 Numerical analysis (65-XX) 24 Systems theory; control (93-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 19 Mechanics of particles and systems (70-XX) 19 Fluid mechanics (76-XX) 16 Biology and other natural sciences (92-XX) 13 Dynamical systems and ergodic theory (37-XX) 10 Integral equations (45-XX) 10 Mechanics of deformable solids (74-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Operator theory (47-XX) 3 Approximations and expansions (41-XX) 3 Probability theory and stochastic processes (60-XX) 2 Potential theory (31-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Mathematical logic and foundations (03-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Operations research, mathematical programming (90-XX)

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