G. V. Alekseev, A. M. Khludnev, “The stability of solutions to extremal problems of boundary control for stationary heat convection equations”, Sib. Zh. Ind. Mat., 13:2 (2010), 5–18; J. Appl. Industr. Math., 5:1 (2011), 1

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Sibirskii Zhurnal Industrial'noi Matematiki, 2010, Volume 13, Number 2, Pages 5–18 (Mi sjim605)

This article is cited in 15 scientific papers (total in 15 papers)

The stability of solutions to extremal problems of boundary control for stationary heat convection equations

G. V. Alekseev^a, A. M. Khludnev^b

^a Applied Mathematics Institute, FEB RAS, Vladivostok
^b Lavrent'ev Institute of Hydrodynamics, SB RAS, Novosibirsk

Full-text PDF (285 kB) Citations (15)

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Abstract: We study the extremal problems of boundary control for the stationary heat convection equations with Dirichlet boundary conditions on the velocity and temperature. As cost functionals we choose the mean square deviation of the required temperature field from the temperature field measured in some part of the flow region. The controls are functions involved in the Dirichlet conditions. We prove the stability of solutions under certain perturbations of both the quality functional and one of the known functions involved in the original equations of the model.

Keywords: heat convection, extremal problems, uniqueness, stability estimates.

Received: 25.05.2009

English version:
Journal of Applied and Industrial Mathematics, 2011, Volume 5, Issue 1, Pages 1–13
DOI: https://doi.org/10.1134/S1990478911010017

Bibliographic databases:

Document Type: Article

UDC: 517.95

Language: Russian

Citation: G. V. Alekseev, A. M. Khludnev, “The stability of solutions to extremal problems of boundary control for stationary heat convection equations”, Sib. Zh. Ind. Mat., 13:2 (2010), 5–18; J. Appl. Industr. Math., 5:1 (2011), 1–13

Citation in format AMSBIB

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\crossref{https://doi.org/10.1134/S1990478911010017}

Linking options:

https://www.mathnet.ru/eng/sjim605

https://www.mathnet.ru/eng/sjim/v13/i2/p5

This publication is cited in the following 15 articles:

E. S. Baranovskii, “The optimal start control problem for two-dimensional Boussinesq equations”, Izv. Math., 86:2 (2022), 221–242
A. A. Domnich, M. A. Artemov, O. Yu. Shishkina, “On the boundary value problem for a model of nonisothermal flows of a non-Newtonian fluid”, J. Appl. Industr. Math., 14:1 (2020), 37–45
Baranovskii E.S., Domnich A.A., “Model of a Nonuniformly Heated Viscous Flow Through a Bounded Domain”, Differ. Equ., 56:3 (2020), 304–314
G. V. Alekseev, Y. E. Spivak, Springer Proceedings in Mathematics & Statistics, 243, Nonlinear and Inverse Problems in Electromagnetics, 2018, 1
Alekseev G.V., Brizitskii R.V., Spivak Yu.E., “Control Approach in Inverse Problems For Time-Harmonic Maxwell Equations Under Mixed Boundary Conditions”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 354–358
Spivak Yu.E., “Optimization Method in Static Magnetic Cloaking Problems”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 1327–1331
Brizitskii R.V., Saritskaya Zh.Yu., “Inverse Coefficient Problems For Static Maxwell Equations”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 1342–1348
Lobanov A.V., Spivak Yu.E., “Numerical Analysis of Problem of Designing Magnetic Bilayer Cloak”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 1362–1366
Saritskaya Zh.Yu., Brizitskii R.V., “Boundary Value and Extremum Problems For the Nonlinear Acoustic Model”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 1367–1371
Alekseev G.V., “Cloaking via Impedance Boundary Condition for the 2-D Helmholtz Equation”, Appl. Anal., 93:2 (2014), 254–268
Romanov V.G., Chirkunov Yu.A., “Nonscattering Acoustic Objects in an Anisotropic Medium of Special Kind”, Dokl. Math., 87:1 (2013), 73–75
Alekseev G.V., “Optimization in Problems of Material-Body Cloaking Using the Wave-Flow Method”, Dokl. Phys., 58:4 (2013), 147–151
G. V. Alekseev, M. A. Shepelov, “On the stability of solutions to coefficient inverse extreme problems for the stationary convection-diffusion equation”, J. Appl. Industr. Math., 7:1 (2013), 1–14
G. V. Alekseev, I. S. Vakhitov, O. V. Soboleva, “Stability estimates in identification problems for the convection-diffusion-reaction equation”, Comput. Math. Math. Phys., 52:12 (2012), 1635–1649
Gennady V. Alekseev, Aleksey Lobanov, Gleb Grenkin, “Numerical Study of Inverse Problems of Nonscattering Anisotropic Shell Theory”, AMM, 249-250 (2012), 557

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Сибирский журнал индустриальной математики

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