Edit Profile (opens in new tab) Danilin, Alekseĭ Rufimovich Co-Author Distance Author ID: danilin.aleksei-rufimovich Published as: Danilin, A. R.; Danilin, Alekseĭ Rufimovich Documents Indexed: 63 Publications since 1975, including 2 Books 1 Contribution as Editor Co-Authors: 10 Co-Authors with 36 Joint Publications 123 Co-Co-Authors all top 5 Co-Authors 28 single-authored 11 Kovrizhnykh, Ol’ga Olegovna 6 Shaburov, Aleksandr Aleksandrovich 6 Tanana, Vitaly Pavlovich 5 Il’in, Arlen Mikhaĭlovich 3 Parysheva, Yu. V. 2 Zorin, A. P. 1 Gustomesov, V. A. 1 Korobitsyna, N. S. 1 Korzunin, L. G. 1 Zakharov, Sergeĭ Viktorovich all top 5 Serials 16 Proceedings of the Steklov Institute of Mathematics 6 Doklady Mathematics 5 Differential Equations 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 3 U.S.S.R. Computational Mathematics and Mathematical Physics 3 Sbornik: Mathematics 2 Differential Equations 2 Computational Mathematics and Mathematical Physics 2 Russian Mathematics 2 Izvestiya Instituta Matematiki i Informatiki. Udmurtskiĭ Gosudarstvennyĭ Universitet 1 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 1 Differentsial’nye Uravneniya 1 Soviet Mathematics. Doklady 1 Soviet Mathematics 1 Automation and Remote Control 1 Journal of Computer and Systems Sciences International 1 Journal of Mathematical Sciences (New York) 1 Fundamental’naya i Prikladnaya Matematika 1 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 1 Matematicheskie Zapiski, Sverdlovsk 1 Ufimskiĭ Matematicheskiĭ Zhurnal all top 5 Fields 41 Calculus of variations and optimal control; optimization (49-XX) 20 Systems theory; control (93-XX) 16 Partial differential equations (35-XX) 13 Numerical analysis (65-XX) 12 Ordinary differential equations (34-XX) 10 Operator theory (47-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of particles and systems (70-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 32 Publications have been cited 126 times in 71 Documents Cited by ▼ Year ▼ Asymptotic methods in analysis. (Асимптотические методы в анализе.) Zbl 1211.34003 Il’in, A. M.; Danilin, A. R. 31 2009 On the structure of the solution of a perturbed time-optimal control problem. Zbl 0967.49001 Danilin, A. R.; Il’in, A. M. 12 1998 Time-optimal control of a small mass point without environmental resistance. Zbl 1276.49003 Danilin, A. R.; Kovrizhnykh, O. O. 11 2013 Asymptotic behaviour of bounded controls for a singular elliptic problem in a domain with a small cavity. Zbl 0934.49017 Danilin, A. R. 9 1998 Approximation of a singularly perturbed elliptic problem of optimal control. Zbl 0983.49018 Danilin, A. R. 7 2000 Asymptotics of a solution to an optimal boundary control problem. Zbl 1251.49003 Danilin, A. R.; Zorin, A. P. 6 2010 Asymptotics of the optimal cost functional in a linear optimal control problem. Zbl 1190.49039 Danilin, A. R.; Parysheva, Yu. V. 5 2009 Asymptotics of the optimal value of the performance functional for a rapidly stabilizing indirect control in the regular case. Zbl 1131.49020 Danilin, A. R. 4 2006 Asymptotics of controls for a singular elliptic problem. Zbl 1080.49502 Danilin, A. R. 3 1999 Asymptotics of the solution in a problem of optimal boundary control of a flow through a part of the boundary. Zbl 1343.49006 Danilin, A. R. 3 2016 Asymptotic expansion of solution to singularly perturbed optimal control problem with convex integral quality functional with terminal part depending on slow and fast variables. Zbl 1463.49051 Danilin, Alekseĭ Rufimovich; Shaburov, Aleksandr Aleksandrovich 3 2019 Asymptotic representation of a solution to a singular perturbation linear time-optimal problem. Zbl 1286.49004 Danilin, A. R.; Kovrizhnykh, O. O. 3 2013 The asymptotical behavior of the solution to the time-optimal problem for a linear system under perturbation of initial data. Zbl 0911.93042 Danilin, A. R.; Il’in, A. M. 2 1996 Asymptotic expansion of solutions to optimal boundary control problems. Zbl 1229.49030 Danilin, A. R.; Zorin, A. P. 2 2011 The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case. Zbl 1236.49079 Danilin, A. R.; Parysheva, Yu. V. 2 2007 Asymptotics of the optimal time in a singular perturbed linear time-optimal problem. Zbl 1251.49002 Danilin, A. R.; Kovrizhnykh, O. O. 2 2010 Asymptotic behaviour of solutions of a singular elliptic system in a rectangle. Zbl 1071.35045 Danilin, A. R. 2 2003 On the asymptotics of the solution of a system of linear equations with two small parameters. Zbl 1170.34039 Danilin, A. R.; Kovrizhnykh, O. O. 2 2008 Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints. Zbl 1302.49002 Danilin, A. R.; Korobitsyna, N. S. 2 2014 Asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with integral constraint. Zbl 1336.49003 Danilin, A. R. 2 2015 Asymptotic behavior of the optimal cost functional for a rapidly stabilizing indirect control in the singular case. Zbl 07811591 Danilin, A. R. 2 2006 Necessary and sufficient conditions for convergence of finite-dimensional approximations of regularized solutions. Zbl 0535.41039 Tanana, V. P.; Danilin, A. R. 1 1982 On the asymptotics of the optimal value of the performance functional in a linear optimal control problem. Zbl 1230.49037 Danilin, A. R.; Parysheva, Yu. V. 1 2011 Approximation of a singularly perturbed elliptic optimal control problem with geometric constraints on the control. Zbl 1122.49304 Danilin, A. R. 1 2003 On estimates optimal with respect to the order of finite-dimensional approximations of solutions of ill-posed problems. Zbl 0585.47053 Danilin, A. R. 1 1985 Application of the concordance method of asymptotic expansions to solving boundary-value problems. Zbl 1084.35008 Il’in, A. M.; Danilin, A. R.; Zakharov, S. V. 1 2003 Differential equations. Textbook. (Differentsial’nye uravneniya. Uchebnoe posobie.) Zbl 0773.34002 Gustomesov, V. A.; Danilin, A. R. 1 1990 Asymptotics of the optimal time in a time-optimal problem with two small parameters. Zbl 1321.49002 Danilin, A. R.; Kovrizhnykh, O. O. 1 2015 Asymptotics of the solution of a bisingular optimal boundary control problem in a bounded domain. Zbl 1414.35043 Danilin, A. R. 1 2018 Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control. Zbl 1523.49017 Danilin, A. R.; Shaburov, A. A. 1 2022 Asymptotics of the solution of a singular optimal distributed control problem in a convex domain. Zbl 1400.35097 Danilin, A. R. 1 2018 Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables. Zbl 1457.49023 Danilin, Alekseĭ Rufimovich; Shaburov, Aleksandr Aleksandrovich 1 2020 Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control. Zbl 1523.49017 Danilin, A. R.; Shaburov, A. A. 1 2022 Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables. Zbl 1457.49023 Danilin, Alekseĭ Rufimovich; Shaburov, Aleksandr Aleksandrovich 1 2020 Asymptotic expansion of solution to singularly perturbed optimal control problem with convex integral quality functional with terminal part depending on slow and fast variables. Zbl 1463.49051 Danilin, Alekseĭ Rufimovich; Shaburov, Aleksandr Aleksandrovich 3 2019 Asymptotics of the solution of a bisingular optimal boundary control problem in a bounded domain. Zbl 1414.35043 Danilin, A. R. 1 2018 Asymptotics of the solution of a singular optimal distributed control problem in a convex domain. Zbl 1400.35097 Danilin, A. R. 1 2018 Asymptotics of the solution in a problem of optimal boundary control of a flow through a part of the boundary. Zbl 1343.49006 Danilin, A. R. 3 2016 Asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with integral constraint. Zbl 1336.49003 Danilin, A. R. 2 2015 Asymptotics of the optimal time in a time-optimal problem with two small parameters. Zbl 1321.49002 Danilin, A. R.; Kovrizhnykh, O. O. 1 2015 Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints. Zbl 1302.49002 Danilin, A. R.; Korobitsyna, N. S. 2 2014 Time-optimal control of a small mass point without environmental resistance. Zbl 1276.49003 Danilin, A. R.; Kovrizhnykh, O. O. 11 2013 Asymptotic representation of a solution to a singular perturbation linear time-optimal problem. Zbl 1286.49004 Danilin, A. R.; Kovrizhnykh, O. O. 3 2013 Asymptotic expansion of solutions to optimal boundary control problems. Zbl 1229.49030 Danilin, A. R.; Zorin, A. P. 2 2011 On the asymptotics of the optimal value of the performance functional in a linear optimal control problem. Zbl 1230.49037 Danilin, A. R.; Parysheva, Yu. V. 1 2011 Asymptotics of a solution to an optimal boundary control problem. Zbl 1251.49003 Danilin, A. R.; Zorin, A. P. 6 2010 Asymptotics of the optimal time in a singular perturbed linear time-optimal problem. Zbl 1251.49002 Danilin, A. R.; Kovrizhnykh, O. O. 2 2010 Asymptotic methods in analysis. (Асимптотические методы в анализе.) Zbl 1211.34003 Il’in, A. M.; Danilin, A. R. 31 2009 Asymptotics of the optimal cost functional in a linear optimal control problem. Zbl 1190.49039 Danilin, A. R.; Parysheva, Yu. V. 5 2009 On the asymptotics of the solution of a system of linear equations with two small parameters. Zbl 1170.34039 Danilin, A. R.; Kovrizhnykh, O. O. 2 2008 The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case. Zbl 1236.49079 Danilin, A. R.; Parysheva, Yu. V. 2 2007 Asymptotics of the optimal value of the performance functional for a rapidly stabilizing indirect control in the regular case. Zbl 1131.49020 Danilin, A. R. 4 2006 Asymptotic behavior of the optimal cost functional for a rapidly stabilizing indirect control in the singular case. Zbl 07811591 Danilin, A. R. 2 2006 Asymptotic behaviour of solutions of a singular elliptic system in a rectangle. Zbl 1071.35045 Danilin, A. R. 2 2003 Approximation of a singularly perturbed elliptic optimal control problem with geometric constraints on the control. Zbl 1122.49304 Danilin, A. R. 1 2003 Application of the concordance method of asymptotic expansions to solving boundary-value problems. Zbl 1084.35008 Il’in, A. M.; Danilin, A. R.; Zakharov, S. V. 1 2003 Approximation of a singularly perturbed elliptic problem of optimal control. Zbl 0983.49018 Danilin, A. R. 7 2000 Asymptotics of controls for a singular elliptic problem. Zbl 1080.49502 Danilin, A. R. 3 1999 On the structure of the solution of a perturbed time-optimal control problem. Zbl 0967.49001 Danilin, A. R.; Il’in, A. M. 12 1998 Asymptotic behaviour of bounded controls for a singular elliptic problem in a domain with a small cavity. Zbl 0934.49017 Danilin, A. R. 9 1998 The asymptotical behavior of the solution to the time-optimal problem for a linear system under perturbation of initial data. Zbl 0911.93042 Danilin, A. R.; Il’in, A. M. 2 1996 Differential equations. Textbook. (Differentsial’nye uravneniya. Uchebnoe posobie.) Zbl 0773.34002 Gustomesov, V. A.; Danilin, A. R. 1 1990 On estimates optimal with respect to the order of finite-dimensional approximations of solutions of ill-posed problems. Zbl 0585.47053 Danilin, A. R. 1 1985 Necessary and sufficient conditions for convergence of finite-dimensional approximations of regularized solutions. Zbl 0535.41039 Tanana, V. P.; Danilin, A. R. 1 1982 all cited Publications top 5 cited Publications all top 5 Cited by 55 Authors 26 Danilin, Alekseĭ Rufimovich 9 Kovrizhnykh, Ol’ga Olegovna 9 Shaburov, Aleksandr Aleksandrovich 8 Zakharov, Sergeĭ Viktorovich 4 Tursunov, Dilmurat Abdillazhanovich 2 Ershov, Aleksandr Anatol’evich 2 Gadyl’shin, Timur Rustemovich 2 Il’in, Arlen Mikhaĭlovich 2 Kurina, Galina A. 2 Parysheva, Yu. V. 2 Sidikova, Anna Ivanovna 2 Sushkov, Andreĭ Sergeevich 2 Tursunov, Dilmurat Abdilllajanovich 1 Alymkulov, Keldibay 1 Andrianov, Igor Vasil’evich 1 Anikin, A. Yu. 1 Asylbekov, T. D. 1 Bekmurza uulu, Ybadylla 1 Claeys, Xavier 1 Collino, Francis 1 Danishevskiĭ, Vladislav Valentinovich 1 Dmitriev, Mikhail G. 1 Dobrokhotov, Sergei Yurievich 1 Dolbeeva, S. F. 1 Efimov, Dmitriĭ Yur’evich 1 Erkebaev, Ulukbek Zairbekovich 1 Frolovskaya, Oksana A. 1 Gamkrelidze, Revaz Valerianovich 1 Hoai, Nguyen Thi Xuan 1 Kalashnikova, Margarita A. 1 Kapustyan, Volodymyr Omelyanovich 1 Korobitsyna, N. S. 1 Kozhobekov, Kudaiberdi Gaparalievich 1 Krivopol, V. A. 1 Lee, Chiun-Chang 1 Leont’eva, Anastasiya O. 1 Markeev, Anatoliĭ Pavlovich 1 Mukminov, Farit Khamzaevich 1 Nalimov, Mikhail Yur’evich 1 Nauryzbaev, N. Zh. 1 Nazaikinskii, Vladimir E. 1 Nguyen, Thi Hoai Thuong 1 Pukhnachov, Vladislav Vasil’evich 1 Rogerson, Graham A. 1 Rusanova, Mariya Igor’evna 1 Safarova, Arzu R. 1 Salmanov, Valid F. 1 Shabat, Alekseĭ Borisovich 1 Shamaev, E. V. 1 Shomanova, A. A. 1 Subbotina, Nina N. 1 Tanana, Vitaly Pavlovich 1 Temirgaliev, Nurlan Temirgalievich 1 Tolokonnikov, Lev Alekseevich 1 Tsvetkova, Anna V. all top 5 Cited in 29 Serials 20 Proceedings of the Steklov Institute of Mathematics 4 Mathematical Notes 3 Theoretical and Mathematical Physics 3 Computational Mathematics and Mathematical Physics 3 Automation and Remote Control 3 Russian Mathematics 3 Journal of Mathematical Sciences (New York) 3 Lobachevskii Journal of Mathematics 3 Differential Equations 3 Izvestiya Instituta Matematiki i Informatiki. Udmurtskiĭ Gosudarstvennyĭ Universitet 3 Ural Mathematical Journal 2 Doklady Mathematics 2 Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika 1 Journal of Applied Mathematics and Mechanics 1 Functional Analysis and its Applications 1 Journal of Optimization Theory and Applications 1 Numerische Mathematik 1 Siberian Mathematical Journal 1 Cybernetics and Systems Analysis 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 1 Matematicheskoe Modelirovanie 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Numerical Algebra, Control and Optimization 1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 1 Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki 1 International Journal of Engineering Mathematics 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Cited in 22 Fields 31 Calculus of variations and optimal control; optimization (49-XX) 23 Partial differential equations (35-XX) 22 Ordinary differential equations (34-XX) 18 Systems theory; control (93-XX) 6 Numerical analysis (65-XX) 5 Mechanics of deformable solids (74-XX) 4 Fluid mechanics (76-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 3 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year