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Found 139 Documents (Results 1–100)

Asymptotics of the solution of a singularly perturbed system of equations with a multizone internal layer. (English. Russian original) Zbl 1469.34077

Differ. Equ. 57, No. 4, 415-445 (2021); translation from Differ. Uravn. 57, No. 4, 435-465 (2021).
MSC:  34E15 34B15 34E05
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Asymptotics of a steplike contrast structure in a partially dissipative stationary system of equations. (English. Russian original) Zbl 1466.34054

Comput. Math. Math. Phys. 61, No. 1, 53-79 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 1, 57-84 (2021).
MSC:  34E15 34E05 34B15
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On singularly perturbed systems of ODE with a multiple root of the degenerate equation. (English. Russian original) Zbl 1445.34087

Izv. Math. 84, No. 2, 262-290 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 2, 60-89 (2020).
MSC:  34E15 34E05 34B15
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Asymptotic expansion of the solution to a partially dissipative system of equations with a multizone boundary layer. (English. Russian original) Zbl 1443.34054

Comput. Math. Math. Phys. 59, No. 10, 1672-1692 (2019); translation from Zh. Vychisl. Mat. Mat. Fiz. 59, No. 10, 1731-1751 (2019).
MSC:  34E15 34B15 34E05
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Asymptotic behavior and stability of a stationary boundary-layer solution to a partially dissipative system of equations. (English. Russian original) Zbl 1430.35014

Comput. Math. Math. Phys. 59, No. 7, 1148-1171 (2019); translation from Zh. Vychisl. Mat. Mat. Fiz. 59, No. 7, 1201-1229 (2019).
MSC:  35B25 35G55 35B40
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On one singularly perturbed system of ordinary differential equations with multiple root of the degenerate equation. (English. Russian original) Zbl 1440.34059

J. Math. Sci., New York 240, No. 3, 224-248 (2019); translation from Neliniĭni Kolyvannya 21, No. 1, 6-28 (2018).
MSC:  34E05 34E15 34B15
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Asymptotics of a Spike type contrast structure in a problem with a multiple root of the degenerate equation. (English. Russian original) Zbl 1460.34070

Differ. Equ. 55, No. 6, 758-775 (2019); translation from Differ. Uravn. 55, No. 6, 774-791 (2019).
MSC:  34E05 34B15 34E15
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On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer. (English. Russian original) Zbl 1397.35011

Comput. Math. Math. Phys. 58, No. 6, 925-949 (2018); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 6, 961-987 (2018).
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Asymptotic behaviour and stability of solutions of a singularly perturbed elliptic problem with a triple root of the degenerate equation. (English. Russian original) Zbl 1373.35026

Izv. Math. 81, No. 3, 481-504 (2017); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 3, 21-44 (2017).
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Asymptotics of the solution to a singularly perturbed elliptic problem with a three-zone boundary layer. (English. Russian original) Zbl 1362.35029

Comput. Math. Math. Phys. 56, No. 8, 1414-1425 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 8, 1428-1440 (2016).
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Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation. (English. Russian original) Zbl 1361.35085

Sb. Math. 207, No. 8, 1100-1126 (2016); translation from Mat. Sb. 207, No. 7, 73-100 (2016).
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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. (English. Russian original) Zbl 1350.35013

Comput. Math. Math. Phys. 56, No. 4, 593-611 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 4, 605-624 (2016).
MSC:  35B25 35K20 35K58
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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. (English. Russian original) Zbl 1347.34093

Math. Notes 99, No. 2, 210-221 (2016); translation from Mat. Zametki 99, No. 2, 201-214 (2016).
MSC:  34E05 34B15 34E15
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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. (English. Russian original) Zbl 1517.34082

Differ. Equ. 51, No. 12, 1569-1582 (2015); translation from Differ. Uravn. 51, No. 12, 1593-1605 (2015).
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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. (English. Russian original) Zbl 1295.35032

Differ. Equ. 49, No. 10, 1261-1273 (2013); translation from Differ. Uravn. 49, No. 10, 1295-1307 (2013).
MSC:  35B25 35K20 35K58
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A step-like contrast structure in a singularly perturbed system of elliptic equations. (Russian, English) Zbl 1299.35027

Zh. Vychisl. Mat. Mat. Fiz. 53, No. 9, 1427-1447 (2013); translation in Comput. Math. Math. Phys. 53, No. 9, 1239-1259 (2013).
MSC:  35B25 35B40 35J25
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A singularly perturbed elliptic problem in the case of a multiple root of the degenerate equation. (Russian, English) Zbl 1299.35026

Zh. Vychisl. Mat. Mat. Fiz. 53, No. 8, 1291-1301 (2013); translation in Comput. Math. Math. Phys. 53, No. 8, 1117-1127 (2013).
MSC:  35B25 35B40 35J25
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On the special properties of the boundary layer in singularly perturbed problems with multiple root of the degenerate equation. (English. Russian original) Zbl 1284.34099

Math. Notes 94, No. 1, 60-70 (2013); translation from Mat. Zametki 94, No. 1, 68-80 (2013).
MSC:  34E05 34B15 34E15
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Steplike contrast structure in a singularly perturbed system of equations with different powers of a small parameter. (Russian, English) Zbl 1274.35014

Zh. Vychisl. Mat. Mat. Fiz. 52, No. 11, 1983-2003 (2012); translation in Comput. Math. Math. Phys. 52, No. 11, 1526-1546 (2012).
MSC:  35B25 35B40 35B36
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On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation. (Russian, English) Zbl 1224.35225

Zh. Vychisl. Mat. Mat. Fiz. 51, No. 1, 44-55 (2011); translation in Comput. Math. Math. Phys. 51, No. 1, 40-50 (2011).
MSC:  35K65 35B10 35B25
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Singularly perturbed problems with boundary and internal layers. (English. Russian original) Zbl 1207.35039

Proc. Steklov Inst. Math. 268, 258-273 (2010); translation from Trudy Mat. Inst. Steklova 268, 268-283 (2010).
MSC:  35B25 35K10
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On a singularly perturbed system of two second-order equations in the case of intersecting roots of the degenerate equation. (English. Russian original) Zbl 1190.34016

Differ. Equ. 45, No. 7, 933-950 (2009); translation from Differ. Uravn. 45, No. 7, 915-931 (2009).
MSC:  34B15 34E15 34E05
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On a singularly perturbed first-order partial differential equation in the case of intersecting roots of the degenerate equation. (English. Russian original) Zbl 1180.35046

Differ. Equ. 45, No. 2, 186-196 (2009); translation from Differ. Uravn. 45, No. 2, 180-190 (2009).
MSC:  35B25 35F31
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Singularly perturbed two-dimensional parabolic problem in the case of intersecting roots of the reduced equation. (Russian, English) Zbl 1210.35140

Zh. Vychisl. Mat. Mat. Fiz. 47, No. 4, 646-654 (2007); translation in Comput. Math. Math. Phys. 46, No. 4, 620-628 (2007).
MSC:  35K10 35B20
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On singularly perturbed problems in the case of intersecting roots of the degenerate equation. (English, Russian) Zbl 1159.35307

Mosc. Univ. Comput. Math. Cybern. 2006, No. 3, 60-67 (2006); translation from Vestn. Mosk. Univ., Ser. XV 2006, No. 3, 59-65 (2006).
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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. (English. Russian original) Zbl 1279.34067

Differ. Equ. 42, No. 2, 237-248 (2006); translation from Differ. Uravn. 42, No. 2, 221-232 (2006).
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On a singularly perturbed system of first-order partial differential equations with various degrees of a small parameter. (English. Russian original) Zbl 1140.35004

Differ. Equ. 42, No. 6, 826-841 (2006); translation from Differ. Uravn. 42, No. 6, 775-789 (2006).
MSC:  35B25 35K50 35K55
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On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic equation. (Russian, English) Zbl 1210.35147

Zh. Vychisl. Mat. Mat. Fiz. 46, No. 3, 433-444 (2006); translation in Comput. Math. Math. Phys. 46, No. 3, 413-424 (2006).
MSC:  35K20 35B25
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Singular perturbation elliptic boundary-value problems in the case of a nonisolated root of the degenerate equation. (English. Russian original) Zbl 1094.35023

Math. Notes 78, No. 1, 23-32 (2005); translation from Mat. Zametki 78, No. 1, 26-36 (2005).
MSC:  35B25 35J25
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Global domain of attraction of a step-like contrast structure in a critical case. (Russian, English) Zbl 1210.35144

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 8, 1410-1431 (2004); translation in Comput. Math. Math. Phys. 44, No. 8, 1334-1355 (2004).
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On the global domain of influence of stable steplike contrast structures in the Dirichlet problem. (Russian, English) Zbl 1072.35538

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 6, 1039-1061 (2004); translation in Comput. Math. Math. Phys. 44, No. 6, 985-1006 (2004).
MSC:  35K55 35B25 35B40
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On the formation of a solution with an internal layer in a parabolic system with different Powers of a small parameter. (English. Russian original) Zbl 1068.35011

Differ. Equ. 40, No. 3, 382-395 (2004); translation from Differ. Uravn. 40, No. 3, 356-367 (2004).
MSC:  35B25 35K60 35K50
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Singularly perturbed parabolic problem in the case of intersecting roots of the degenerate equation. (English) Zbl 1125.35313

Danilin, A. R. (ed.), Asymptotic expansions, approximation theory, topology. Transl. from the Russian. Moscow: Maik Nauka / Interperiodica. Proceedings of the Steklov Institute of Mathematics 2003, Suppl. 1, S37-S44 (2003).
MSC:  35B25 35K55 35K60
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Asymptotic behavior of the solution of a singularly perturbed system of reaction-diffusion equations in a thin rod. (Russian, English) Zbl 1136.35402

Zh. Vychisl. Mat. Mat. Fiz. 43, No. 8, 1160-1182 (2003); translation in Comput. Math. Math. Phys. 43, No. 8, 1109-1131 (2003).
MSC:  35K55 35B25 35B40
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System of singularly perturbed equations in the case of intersecting roots of a degenerate system. (Russian, English) Zbl 1079.34530

Zh. Vychisl. Mat. Mat. Fiz. 42, No. 11, 1686-1699 (2002); translation in Comput. Math. Math. Phys. 42, No. 11, 1622-1635 (2002).
MSC:  34E15 34E05 34B15
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On a singularly perturbed system of parabolic equations in the case of intersecting roots of the degenerate equation. (Russian, English) Zbl 1055.35015

Zh. Vychisl. Mat. Mat. Fiz. 42, No. 2, 185-196 (2002); translation in Comput. Math. Math. Phys. 42, No. 2, 176-187 (2002).
MSC:  35B25 35K40 35K50 35K57
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The stability of a step-like contrast structure in the case of a multiple root of the equation for the transition point. (English. Russian original) Zbl 1039.35014

Differ. Equ. 38, No. 1, 75-86 (2002); translation from Differ. Uravn. 38, No. 1, 70-80 (2002).
MSC:  35B25 35K60 35C20
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On the global domain of influence of stable solutions with interior layers in the two-dimensional case. (English. Russian original) Zbl 1091.35037

Izv. Math. 66, No. 1, 1-40 (2002); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 1, 3-42 (2002).
Reviewer: Jiaqi Mo (Wuhu)
MSC:  35K57 35B25 35B40
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Boundary value problem for a system of fast and slow second-order equations in the case of intersecting roots of the degenerate equation. (English. Russian original) Zbl 1036.34061

Comput. Math. Math. Phys. 41, No. 8, 1108-1121 (2001); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 8, 1165-1179 (2001).
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Global influence domains of stable solutions with internal layers. (English. Russian original) Zbl 1009.35008

Sb. Math. 192, No. 5, 651-691 (2001); translation from Mat. Sb. 192, No. 5, 13-53 (2001).
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A two-dimensional step-like contrast structure in the case of a multiple root of the transition line equation. (English. Russian original) Zbl 1007.35028

Differ. Equ. 37, No. 4, 524-539 (2001); translation from Differ. Uravn. 37, No. 4, 495-510 (2001).
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A step-like contrast structure for the case of a multiple root of the transition point equation (the critical case). (English. Russian original) Zbl 1013.34056

Differ. Equ. 37, No. 2, 185-194 (2001); translation from Differ. Uravn. 37, No. 2, 171-180 (2001).
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On the global domain of influence of solutions with internal layers. (English. Russian original) Zbl 1050.35007

Dokl. Math. 62, No. 1, 26-27 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 373, No. 2, 155-156 (2000).
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A limit theorem for a Tikhonov system of equations. (English. Russian original) Zbl 0999.34056

Comput. Math. Math. Phys. 40, No. 5, 669-679 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 5, 703-713 (2000).
MSC:  34E15 34D15
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A steplike contrast structure in a singularly perturbed system of elliptic equations with different power of a small parameter. (English. Russian original) Zbl 0993.35036

Comput. Math. Math. Phys. 40, No. 6, 837-859 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 6, 877-899 (2000).
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Asymptotic stability of solutions of singularly perturbed boundary value problems with boundary and internal layers. (English. Russian original) Zbl 0982.35012

Differ. Equ. 36, No. 2, 224-235 (2000); translation from Differ. Uravn. 36, No. 2, 198-208 (2000).
MSC:  35B25 35K60 35B30
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Existence, local uniqueness, and asymptotics of two-dimensional periodic steplike contrast structures. (English. Russian original) Zbl 0965.35074

Comput. Math. Math. Phys. 39, No. 5, 779-798 (1999); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 5, 812-831 (1999).
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A contrast step-like structure in the case of a multiple root of the equation for the transition point. (English. Russian original) Zbl 1040.34519

Differ. Equations 34, No. 8, 1031-1041 (1998); translation from Differ. Uravn. 34, No. 8, 1029-1038 (1998).
MSC:  34E15 34E05
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A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability. (English. Russian original) Zbl 0920.34023

Math. Notes 63, No. 3, 311-318 (1998); translation from Mat. Zametki 63, No. 3, 354-362 (1998).
MSC:  34B15 34E15 34E10
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Spikelike contrast structures in the parabolic system of two singularly perturbed equations. (English. Russian original) Zbl 0940.35023

Comput. Math. Math. Phys. 37, No. 4, 403-416 (1997); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 4, 415-428 (1997).
MSC:  35B25 35C20 35K57 35K50
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Asymptotic behavior of the solution of the heat equation with a nonlinear heat source in a thin rod. (English. Russian original) Zbl 1161.35430

Comput. Math. Math. Phys. 36, No. 6, 743-757 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 6, 68-85 (1996).
MSC:  35K57 35B25 35C20
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Spatially periodic contrast structures in singularly perturbed elliptic problems. (English. Russian original) Zbl 0897.35007

Dokl. Math. 54, No. 3, 942-945 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 6, 731-734 (1996).
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A singularly perturbed “reaction-diffusion-transfer” system which degenerates into a system with a finite equation and a first-order partial differential equation. (English. Russian original) Zbl 0848.35007

Comput. Math. Math. Phys. 35, No. 2, 177-190 (1995); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 2, 223-240 (1995).
MSC:  35B25 35K50 35K55
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One singularly perturbed system of partial differential equations of the first order. (English. Russian original) Zbl 0859.35007

Math. Notes 57, No. 3, 240-247 (1995); translation from Mat. Zametki 57, No. 3, 338-349 (1995).
MSC:  35B25 35F05
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The boundary function method for singular perturbation problems. (English) Zbl 0823.34059

SIAM Studies in Applied Mathematics. 14. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xiii, 256 p. (1995).
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A singulary perturbed “reaction-diffusion-transfer” system which degenerates into a system of two first-order differential equations. (English. Russian original) Zbl 0839.35063

Comput. Math. Math. Phys. 34, No. 10, 1197-1213 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 10, 1380-1400 (1994).
Reviewer: L.Kalyakin (Ufa)
MSC:  35K60 35B25 35C20
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Contrast structures: Theory and applications. (English. Russian original) Zbl 0904.35007

Comput. Math. Model. 6, No. 4, 231-234 (1995); translation from Matematicheskoe Modelirovanie, Moscow University, Moscow, 1993, 63-67 (1993).
MSC:  35B25 35J65 35B40
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The contrast structure type solutions of nonlinear singularly perturbed equations. (English) Zbl 0795.35036

Mathematical modelling and applied mathematics, Proc. IMACS Int. Conf., Moscow/USSR 1990, 439-445 (1992).
MSC:  35J65 35B25 35B40
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Smoothing procedure for a singularly perturbed parabolic problem. (English. Russian original) Zbl 0735.35006

Mosc. Univ. Comput. Math. Cybern. 1991, No. 1, 21-27 (1991); translation from Vestn. Mosk. Univ., Ser. XV 1991, No. 1, 22-29 (1991).
Reviewer: I.Tralle
MSC:  35B25 35K60 35A35
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Asymptotic methods in the theory of singular perturbations. (Асимптотические методы в теории сингулярных возмущений.) (Russian) Zbl 0747.34033

Aktual’nye Voprosy Prikladnoĭ i Vychislitel’noĭ Matematiki. Moskva: Vysshaya Shkola. 208 p. (1990).
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A smoothing procedure in a system of singularly perturbed parabolic equations. (English. Russian original) Zbl 0723.65078

Mosc. Univ. Comput. Math. Cybern. 1989, No. 3, 1-9 (1989); translation from Vestn. Mosk. Univ., Ser. XV 1989, No. 3, 5-13 (1989).
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Asymptotic approximation of the solution of a singularly perturbed parabolic two-dimensional problem with a nonsmooth limit solution. (English. Russian original) Zbl 0714.35007

Differ. Equations 25, No. 12, 1514-1518 (1989); translation from Differ. Uravn. 25, No. 12, 2128-2133 (1989).
Reviewer: G.Boillat
MSC:  35B25 35K20
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Asymptotics of a solution of a singularly perturbed parabolic problem in the two-dimensional case. (English. Russian original) Zbl 0688.35031

Differ. Equations 25, No. 3, 315-322 (1989); translation from Differ. Uravn. 25, No. 3, 453-461 (1989).
Reviewer: V.F.Butuzov
MSC:  35K20 35B25
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Asymptotic behaviour of the solution of the problem of combustion in the case of an autocatalytic reaction. (English. Russian original) Zbl 0689.35018

U.S.S.R. Comput. Math. Math. Phys. 28, No. 3, 39-47 (1988); translation from Zh. Vychisl. Mat. Mat. Fiz. 28, No. 5, 683-694 (1988).
Reviewer: M.Fila
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On a singularly perturbed quasilinear parabolic problem with unsmooth corner boundary functions. (English. Russian original) Zbl 0711.35009

U.S.S.R. Comput. Math. Math. Phys. 27, No. 4, 33-39 (1987); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 7, 1012-1021 (1987).
MSC:  35B25 35K55
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