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Found 130 Documents (Results 1–100)

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Approximate feedback control for hyperbolic boundary-value problem with rapidly oscillating coefficients in the case of non-convex objective functional. (English) Zbl 1478.49035

Sadovnichiy, Victor A. (ed.) et al., Contemporary approaches and methods in fundamental mathematics and mechanics. Cham: Springer. Underst. Complex Syst., 407-415 (2021).
MSC:  49N35
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Approximate minimax estimation of functionals of solutions to the wave equation under nonlinear observations. (English. Russian original) Zbl 1454.35018

Cybern. Syst. Anal. 56, No. 5, 793-801 (2020); translation from Kibern. Sist. Anal. 2020, No. 5, 126-135 (2020).
MSC:  35B27 35L20
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Application of the averaging method to the problems of optimal control for ordinary differential equations on the semiaxis. (English. Ukrainian original) Zbl 1418.49021

Ukr. Math. J. 70, No. 5, 739-753 (2018); translation from Ukr. Mat. Zh. 70, No. 5, 642-654 (2018).
MSC:  49K15 34K26
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Operator-norm convergence estimates for elliptic homogenization problems on periodic singular structures. (English. Russian original) Zbl 1402.35029

J. Math. Sci., New York 232, No. 4, 558-572 (2018); translation from Probl. Mat. Anal. 93, 137-148 (2018).
MSC:  35B27 35B25 35J15
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Homogenization of hyperbolic equations. (English. Russian original) Zbl 1370.35037

Funct. Anal. Appl. 50, No. 4, 319-324 (2016); translation from Funkts. Anal. Prilozh. 50, No. 4, 91-96 (2016).
MSC:  35B27 35L20 35Q74
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Homogenization of elliptic systems with periodic coefficients: operator error estimates in \(L_{2}(\mathbb{R}^{d})\) with corrector taken into account. (English. Russian original) Zbl 1316.35024

St. Petersbg. Math. J. 26, No. 4, 643-693 (2015); translation from Algebra Anal. 26, No. 4, 195-263 (2014).
MSC:  35B27 35J47 35J10
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Optimal integration of rapidly oscillating functions in the class \(W_{2,L,N}\) with the use of different information operators. (English. Russian original) Zbl 1303.65011

Cybern. Syst. Anal. 49, No. 2, 229-238 (2013); translation from Kibern. Sist. Anal. 2013, No. 2, 83-93 (2013).
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Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source. (English. Russian original) Zbl 1293.35279

Proc. Steklov Inst. Math. 281, 161-178 (2013); translation from Tr. Mat. Inst. Steklova 281, 170-187 (2013); corrigendum Proc. Steklov Inst. Math. 288, 265 (2015); translation from Tr. Mat. Inst. Steklova 288, 287 (2015).
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Using reserves for computation optimization to improve the integration of rapidly oscillating functions. (English. Russian original) Zbl 1302.65291

Cybern. Syst. Anal. 47, No. 4, 613-630 (2011); translation from Kibern. Sist. Anal. 2011, No. 4, 125-145 (2011).
MSC:  65T40 42A16
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Asymptotic integration of a system of differential equations with a large parameter in the critical case. (Russian, English) Zbl 1249.34123

Zh. Vychisl. Mat. Mat. Fiz. 51, No. 6, 1043-1055 (2011); translation in Comput. Math. Math. Phys. 51, No. 6, 975-986 (2011).
MSC:  34C25 34E10
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Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign density. (English. Russian original) Zbl 1221.35258

J. Math. Sci., New York 169, No. 2, 212-248 (2010); translation from Probl. Mat. Anal. 48, 74-107 (2010).
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Optimal quadrature evaluation of integrals of rapidly oscillating functions in Lipschitz interpolation class in case of strong oscillation. (English. Russian original) Zbl 1221.65349

Cybern. Syst. Anal. 46, No. 2, 264-270 (2010); translation from Kibern. Sist. Anal. 2010, No. 2, 105-112 (2010).
MSC:  65T40 42A16
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Homogenization with corrector for a periodic elliptic operator near an edge of inner gap. (English. Russian original) Zbl 1207.35048

J. Math. Sci., New York 159, No. 2, 264-280 (2009); translation from Probl. Mat. Anal. 41, 127-142 (2009).
MSC:  35B27 47F05
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Homogenization of periodic second order differential operators including first order terms. (English) Zbl 1169.35310

Suslina, T. (ed.) et al., Spectral theory of differential operators. M. Sh. Birman 80th anniversary collection. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4738-1/hbk). Translations. Series 2. American Mathematical Society 225; Advances in the Mathematical Sciences 62, 227-252 (2008).
MSC:  35B27 47F05 35J45
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The limit absorption principle and homogenization procedure for periodic elliptic operators. (English) Zbl 1177.35027

Funct. Anal. Appl. 42, No. 4, 336-339 (2008); translation from Funkts. Anal. Prilozh. 42, No. 4, 105-108 (2008).
MSC:  35B27
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Homogenization of elliptic systems with periodic coefficients: weighted \(L^p\) and \(L^{\infty}\) estimates for asymptotic remainders. (English. Russian original) Zbl 1135.35016

St. Petersbg. Math. J. 18, No. 2, 269-304 (2007); translation from Algebra Anal. 18, No. 2, 117-166 (2006).
MSC:  35B27 35A08 35J55 74Q05
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Homogenization with corrector term for periodic elliptic differential operators. (English) Zbl 1175.35007

St. Petersbg. Math. J. 17, No. 6, 897-973 (2006); translation from Algebra Anal. 17, No. 6, 1-104 (2005).
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Some topics on the control and homogenization of parabolic partial differential equations. (English) Zbl 1052.35020

Carbone, Luciano (ed.) et al., Homogenization 2001. Proceedings of the first HMS2000 international school and conference on homogenization, Naples, Italy, June 18–22 and 23–27, 2001. Tokyo: Gakkotosho (ISBN 4-7625-0427-0/hbk). GAKUTO Int. Ser., Math. Sci. Appl. 18, 49-93 (2003).
MSC:  35B27 35K20 49J20 35B37
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Power boundary layers in the averaging problem for a scalar equation degenerate on the boundary. (English. Russian original) Zbl 1060.35014

J. Math. Sci., New York 107, No. 3, 3874-3910 (2001); translation from Probl. Mat. Anal. 23, 94-146 (2001).
MSC:  35B27 35C20 35J25
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A generalized interpolation and its application to a generalized finite element method. (English. Chinese original) Zbl 0952.65058

Chin. J. Numer. Math. Appl. 22, No. 2, 84-92 (2000); translation from Math. Numer. Sin. 22, No. 1, 113-120 (2000).
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Homogenization of parabolic equations with contrasting coefficients. (English. Russian original) Zbl 0967.35016

Izv. Math. 63, No. 5, 1015-1061 (1999); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 63, No. 4, 179-224 (1999).
MSC:  35B27 35K57 35K60
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Some new results related to the null controllability of the 1-D heat equation. (English) Zbl 1059.93058

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Optimal control problems in homogenization. (English) Zbl 0912.35019

Équations aux dérivées partielles et applications. Articles dédiés à Jacques-Louis Lions. Gauthier-Villars: Paris. 597-609 (1998).
MSC:  35B27 35B37
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High-order asymptotics of the solution of a problem of optimal control of a distributed system with rapidly oscillating coefficients. (English. Ukrainian original) Zbl 0938.49017

Ukr. Math. J. 48, No. 7, 1063-1073 (1996); translation from Ukr. Mat. Zh. 48, No. 7, 940-948 (1996).
MSC:  49K20 49K40 49N30 80A20
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The asymptotic expansion of the solution to the Cauchy problem for a parabolic equation in a perforated space. (English. Russian original) Zbl 0917.35009

J. Math. Sci., New York 85, No. 6, 2308-2325 (1997); translation from Tr. Semin. Im. I. G. Petrovskogo 19, 109-137 (1996).
MSC:  35B27 35C20 35K15
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On the convergence of solutions of parabolic equations with rapidly oscillating coefficients in perforated domains. (English. Russian original) Zbl 0844.35008

J. Math. Sci., New York 75, No. 3, 1631-1645 (1995); translation from Tr. Semin. Im. I. G. Petrovskogo 17, 27-50 (1994).
MSC:  35B27 35K20
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A study of the stability of solutions of linear parabolic equations with nearly constant coefficients and small diffusion. (English. Russian original) Zbl 0786.35067

J. Sov. Math. 60, No. 6, 1742-1764 (1992); translation from Tr. Semin. Im. I. G. Petrovskogo 15, 128-155 (1991).
MSC:  35K10 35B35 34C25
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A generalization of the Fourier integral transformation in boundary-value problems of the mechanics of composites. (English. Russian original) Zbl 0734.73054

Sov. Phys., Dokl. 35, No. 11, 980-982 (1990); translation from Dokl. Akad. Nauk SSSR 315, No. 1, 53-56 (1990).
MSC:  74E30 74S30 42B10
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Averaging of solutions of the Neumann problem for a second-order elliptic equation and systems in elasticity theory with rapidly oscillating periodic coefficients on a perforated domain. (English. Russian original) Zbl 0652.35028

Russ. Math. Surv. 42, No. 6, 237-238 (1987); translation from Usp. Mat. Nauk 42, No. 6, 195-196 (1987).
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Averaging of the mixed problem for a parabolic equation in a perforated domain. (English. Russian original) Zbl 0636.35032

Russ. Math. Surv. 41, No. 4, 185-186 (1986); translation from Usp. Mat. Nauk 41, No. 4(250), 223-224 (1986).
Reviewer: T.O.Shaposhnikova
MSC:  35K20 35B30 35B40
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Convergence of the energy, stress tensors, and frequencies of natural oscillations in averaging problems arising in elasticity theory. (English. Russian original) Zbl 0588.73035

Sov. Phys., Dokl. 29, 157-159 (1984); translation from Dokl. Akad. Nauk SSSR 274, 1329-1333 (1984).
MSC:  74B99
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