Abstract:
The problem of optimal control of solutions of an elliptic equation in a domain with a small cavity is discussed. Uniform asymptotic formulae for the solutions are obtained up to an arbitrary degree of the small parameter by the method of matching asymptotic expansions. Other aspects of the same problem have been considered by Kapustyan.
Citation:
A. R. Danilin, “Asymptotic behaviour of bounded controls for a singular elliptic problem in a domain with a small cavity”, Sb. Math., 189:11 (1998), 1611–1642
\Bibitem{Dan98}
\by A.~R.~Danilin
\paper Asymptotic behaviour of bounded controls for a~singular elliptic problem in a~domain with a~small cavity
\jour Sb. Math.
\yr 1998
\vol 189
\issue 11
\pages 1611--1642
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\crossref{https://doi.org/10.1070/sm1998v189n11ABEH000364}
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Linking options:
https://www.mathnet.ru/eng/sm364
https://doi.org/10.1070/sm1998v189n11ABEH000364
https://www.mathnet.ru/eng/sm/v189/i11/p27
This publication is cited in the following 30 articles:
S. V. Zakharov, “Constructing the asymptotics of a solution of the heat equation from the known asymptotics of the initial function in three-dimensional space”, Sb. Math., 215:1 (2024), 101–118
A. R. Danilin, “Asymptotic expansion for the solution of an optimal boundary control problem in a doubly connected domain with different control intensity on boundary segments”, Comput. Math. Math. Phys., 62:2 (2022), 218–231
Sergey V. Zakharov, “The asymptotics of a solution of the multidimensional heat equation with unbounded initial data”, Ural Math. J., 7:1 (2021), 168–177
Zakharov S.V., “Long-Time Behavior of the Solution of the Cauchy Problem For the Third-Order Airy Equation”, Asymptotic Anal., 116:2 (2020), 139–148
Danilin A.R., “Asymptotics of the Solution of a Singular Optimal Distributed Control Problem With Essential Constraints in a Convex Domain”, Differ. Equ., 56:2 (2020), 251–263
S. V. Zakharov, “Singular points and asymptotics in the singular Cauchy problem for the parabolic equation with a small parameter”, Comput. Math. Math. Phys., 60:5 (2020), 821–832
A. R. Danilin, “Asimptoticheskoe razlozhenie resheniya singulyarno vozmuschennoi zadachi optimalnogo upravleniya s malym koeffitsientom koertsitivnosti”, Tr. IMM UrO RAN, 24, no. 3, 2018, 51–61
A. R. Danilin, “Asymptotics of the solution of a bisingular optimal boundary control problem in a bounded domain”, Comput. Math. Math. Phys., 58:11 (2018), 1737–1747
S. V. Zakharov, “Asymptotic calculation of the heat distribution on a plane”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 243–249
A. R. Danilin, O. O. Kovrizhnykh, “Asimptotika optimalnogo vremeni v odnoi zadache o bystrodeistvii s malym parametrom”, Tr. IMM UrO RAN, 21, no. 1, 2015, 71–80
A. R. Danilin, “Solution asymptotics in a problem of optimal boundary control of a flow through a part of the boundary”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 55–66
A. P. Zorin, “Asimptoticheskoe razlozhenie resheniya zadachi optimalnogo upravleniya ogranichennym potokom na granitse”, Tr. IMM UrO RAN, 19, no. 1, 2013, 115–120
A. R. Danilin, “Optimalnoe granichnoe upravlenie v oblasti s maloi polostyu”, Ufimsk. matem. zhurn., 4:2 (2012), 87–100
A. R. Danilin, O. O. Kovrizhnykh, “Asymptotic representation of a solution to a singular perturbation linear time-optimal problem”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 22–35
A. R. Danilin, A. P. Zorin, “Asimptotika resheniya zadachi optimalnogo granichnogo upravleniya v ogranichennoi oblasti”, Tr. IMM UrO RAN, 18, no. 3, 2012, 75–82
Danilin A.R., Zorin A.P., “Asymptotic Expansion of Solutions to Optimal Boundary Control Problems”, Doklady Mathematics, 84:2 (2011), 665–668
A. R. Danilin, A. P. Zorin, “Asymptotics of a solution to an optimal boundary control problem”, Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S81–S94
A. R. Danilin, Yu. V. Parysheva, “The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S83–S94
S. V. Zakharov, “Heat Distribution in an Infinite Rod”, Math. Notes, 80:3 (2006), 366–371
Danilin, AR, “Asymptotic behavior of the solution to the Cauchy problem for a Hamilton-Jacoby equation depending on a small parameter”, Doklady Mathematics, 73:2 (2006), 214
Citation in format AMSBIB
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