A. B. Vasil'eva, V. F. Butuzov, N. N. Nefedov, “Singularly perturbed problems with boundary and internal layers”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 268–283; Proc. Steklov Inst. Math., 268 (2010), 258

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 268, Pages 268–283 (Mi tm2867)

This article is cited in 84 scientific papers (total in 84 papers)

Singularly perturbed problems with boundary and internal layers

A. B. Vasil'eva, V. F. Butuzov, N. N. Nefedov

Chair of Mathematics, Faculty of Physics, Moscow State University, Moscow, Russia

Full-text PDF (216 kB) Citations (84)

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Abstract: This paper is an expanded version of the talk given by the authors at the International Conference “Differential Equations and Topology” dedicated to the centenary of the birth of L. S. Pontryagin. We present a brief survey and describe new ideas and methods of analysis in the asymptotic theory of solutions with internal layers, which is one of the topical fields of singular perturbation theory.

Received in February 2009

English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 268, Pages 258–273
DOI: https://doi.org/10.1134/S0081543810010189

Bibliographic databases:

Document Type: Article

UDC: 519.624.2

Language: Russian

Citation: A. B. Vasil'eva, V. F. Butuzov, N. N. Nefedov, “Singularly perturbed problems with boundary and internal layers”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 268–283; Proc. Steklov Inst. Math., 268 (2010), 258–273

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This publication is cited in the following 84 articles:

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N. N. Nefedov, “Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems”, Math. Notes, 115:2 (2024), 232–239
Marina Vіra, Mikola Rashevskii, Petro Samusenko, “Asimptotichnі rozv'yazki kraiovikh zadach dlya lіnіinikh singulyarno zburenikh diferentsіalno-algebraïchnikh sistem”, Nelin. Kolyv., 27:1 (2024), 43
S. V. Baranovsky, A. Ya. Bomba, “The diffusion scattering parameters identification for a modified model of viral infection in the conditions of logistic dynamics of immunological cells”, Math. Model. Comput., 11:1 (2024), 59
Qian Yang, Mingkang Ni, “Multiscale study on a class of singularly perturbed system with discontinuous right-hand side and multiple root of the degenerate solution”, Communications in Nonlinear Science and Numerical Simulation, 139 (2024), 108247
Ruixiang Li, Mingkang Ni, “The Internal Layer of Boundary Value Problem for a Class of System of Singularly Perturbed Equations with Discontinuous Right-Hand Side”, Comput. Math. and Math. Phys., 64:10 (2024), 2429
N. N. Nefedov, “Existence and asymptotic behavior of solutions of boundary value problems for Tiknohov-type reaction–diffusion systems in the case of stability exchange”, Math. Notes, 116:6 (2024), 1332–1338
E. P. Kubyshkin, “Averaging Method in the Problem of Constructing Self-Oscillatory Solutions of Distributed Kinetic Systems”, Comput. Math. and Math. Phys., 64:12 (2024), 2868
S. V. Baranovsky, A. Ya. Bomba, “Generalizing the Infectious Disease Model to Account for Sorption Therapy in Conditions of Diffusion Disorders”, Cybern Syst Anal, 59:4 (2023), 601
A. O. Vatulyan, S. A. Nesterov, O. V. Yavruyan, “The Models of Gradient Mechanics and Singularly Perturbed Boundary Value Problems”, Lobachevskii J Math, 44:8 (2023), 3604
D. V. Lukyanenko, R. L. Argun, A. A. Borzunov, A. V. Gorbachev, V. D. Shinkarev, M. A. Shishlenin, A. G. Yagola, “On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types”, Diff Equat, 59:12 (2023), 1734
Qian Yang, Mingkang Ni, “Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation”, Chin. Ann. Math. Ser. B, 44:1 (2023), 81
S. V. Baranovsky, A. Ya. Bomba, “Identification of the parameters of infectious disease model taking into account sorption therapy under the conditions of diffusion perturbations”, Mat. Met. Fiz. Mekh. Polya, 66:1-2 (2023)
Davydova M.A., Zakharova S.A., “Multidimensional Thermal Structures in the Singularly Perturbed Stationary Models of Heat and Mass Transfer With a Nonlinear Thermal Diffusion Coefficient”, J. Comput. Appl. Math., 400 (2022), 113731
Besova M., Kachalov V., “Analytical Aspects of the Theory of Tikhonov Systems”, Mathematics, 10:1 (2022), 72
Yang Q., Ni M., “Asymptotics of the Solution to a Piecewise-Smooth Quasilinear Second-Order Differential Equation”, J. Appl. Anal. Comput., 12:1 (2022), 256–269
Dana Bibulova, Burkhan Kalimbetov, Valeriy Safonov, “Regularized Asymptotic Solutions of a Singularly Perturbed Fredholm Equation with a Rapidly Varying Kernel and a Rapidly Oscillating Inhomogeneity”, Axioms, 11:3 (2022), 141
R. L. Argun, A. V. Gorbachev, D. V. Lukyanenko, M. A. Shishlenin, “Features of numerical reconstruction of a boundary condition in an inverse problem for a reaction–diffusion–advection equation with data on the position of a reaction front”, Comput. Math. Math. Phys., 62:3 (2022), 441–451
N. N. Nefedov, E. I. Nikulin, A. O. Orlov, “Contrast Structures in the Reaction-Diffusion-Advection Problem in the Case of a Weak Reaction Discontinuity”, Russ. J. Math. Phys., 29:1 (2022), 81
N. T. Levashova, N. N. Nefedov, O. A. Nikolaeva, “Solution with an inner transition layer of a two-dimensional boundary value reaction–diffusion–advection problem with discontinuous reaction and advection terms”, Theoret. and Math. Phys., 207:2 (2021), 655–669

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Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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