Inverse problems of reconstruction of coefficients and transport sources in nonlinear heat conduction equations
Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 33-43.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss methods of functional identification, inverse dynamical systems and stepwise suboptimal optimization for solving inverse problems of reconstruction of coefficients, boundary conditions and transport sources in the nonlinear heat conduction equation.
@article{TIMB_2023_31_1_a4,
     author = {V. T. Borukhov and G. M. Zayats and O. I. Kostyukova},
     title = {Inverse problems of reconstruction of coefficients and transport sources in nonlinear heat conduction equations},
     journal = {Trudy Instituta matematiki},
     pages = {33--43},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a4/}
}
TY  - JOUR
AU  - V. T. Borukhov
AU  - G. M. Zayats
AU  - O. I. Kostyukova
TI  - Inverse problems of reconstruction of coefficients and transport sources in nonlinear heat conduction equations
JO  - Trudy Instituta matematiki
PY  - 2023
SP  - 33
EP  - 43
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a4/
LA  - ru
ID  - TIMB_2023_31_1_a4
ER  - 
%0 Journal Article
%A V. T. Borukhov
%A G. M. Zayats
%A O. I. Kostyukova
%T Inverse problems of reconstruction of coefficients and transport sources in nonlinear heat conduction equations
%J Trudy Instituta matematiki
%D 2023
%P 33-43
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a4/
%G ru
%F TIMB_2023_31_1_a4
V. T. Borukhov; G. M. Zayats; O. I. Kostyukova. Inverse problems of reconstruction of coefficients and transport sources in nonlinear heat conduction equations. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 33-43. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a4/

[1] A. N. Tikhonov, V. Ya. Arsenin, Metody resheniya nekorrektnykh zadach, Nauka, M., 1979

[2] A. S. Leonov, Reshenie nekorrektno postavlennykh obratnykh zadach: Ocherk teorii, prakticheskie algoritmy i demonstratsii v MATLAB, Izd-vo Librokom, M., 2016

[3] A. A. Samarskii, P. N. Vabischevich, Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki, Izd-vo LKI, M., 2009

[4] O. A. Liskovets, Variatsionnye metody resheniya neustoichivykh zadach, Nauka i tekhnika, Minsk, 1981

[5] R. E. Kalman, P. Falb, M. Arbib, Ocherki po matematicheskoi teorii sistem, per. s angl., Editorial URSS, M., 2004 | MR

[6] A. V. Babichev, A. G. Butkovskii, S. Pokholainen, K edinoi geometricheskoi teorii upravleniya, Nauka, M., 2001 | MR

[7] V. T. Borukhov, I. V. Gaishun, V. I. Timoshpolskii, Strukturnye svoistva dinamicheskikh sistem i obratnye zadachi matematicheskoi fiziki, Bel. nauka, Minsk, 2009

[8] O. M. Alifanov, E. A. Artyukhin, S. V. Rumyantsev, Ekstremalnye metody resheniya nekorrektnykh zadach, Nauka, M., 1988

[9] M. N. Ozisik, H. R. B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Routledge, 2018 | MR

[10] Yu. M. Matsevityi, E. N. But, Splain-identifikatsiya teplofizicheskikh protsessov, Naukova dumka, Kiev, 2010

[11] V. T. Borukhov, V. I. Timoshpolskii, “Funktsionalnaya identifikatsiya gradientnymi metodami nelineinogo koeffitsienta teploprovodnosti. I. Sopryazhennye operatory”, IFZh, 78:4 (2005), 68–74

[12] V. T. Borukhov, V. I. Timoshpolskii, G. M. Zayats, V. A. Tsurko, “Funktsionalnaya identifikatsiya gradientnymi metodami nelineinogo koeffitsienta teploprovodnosti. II. Chislennoe modelirovanie”, IFZh, 78:4 (2005), 75–81

[13] V. T. Borukhov, V. I. Timoshpolskii, M. L. German, G. M. Zayats, V. A. Tsurko, “Vosstanovlenie nelineinykh koeffitsientov teploprovodnosti metodom funktsionalnoi identifikatsii”, Tr. mezhdunar. konf. «Problemy upravleniya i prilozheniya (tekhnika, proizvodstvo, ekonomika)», v. 1, Upravlenie i optimizatsiya, Minsk, 2005, 120–127

[14] V. T. Borukhov, V. I. Timoshpolskii, G. M. Zayats, E. V. Kalinevich, V. A. Tsurko, “Opredelenie nelineinogo koeffitsienta teploprovodnosti dlya izdelii trubchatoi formy metodom funktsionalnoi identifikatsii”, IFZh, 79:6 (2006), 23–30

[15] V. T. Borukhov, G. M. Zayats, V. A. Tsurko, “Primenenie metoda funktsionalnoi identifikatsii dlya resheniya obratnoi zadachi teploprovodnosti v usloviyakh needinstvennosti”, Tr. 4-i mezhdunar. konf. «Analiticheskie metody analiza i differentsialnykh uravnenii», AMADE-2006, v. 2, Minsk, 2006, 32–37

[16] V. T. Borukhov, G. M. Zayats, V. A. Tsurko, “Identifikatsiya koeffitsienta teploprovodnosti v nelineinom parabolicheskom uravnenii s vozmuschennymi vkhodnymi dannymi”, Informatika, 2008, no. 4, 29–38

[17] V. T. Borukhov, V. A. Tsurko, G. M. Zayats, “The functional identification approach for numerical reconstruction of the temperature-dependent thermal-conductivity coefficient”, Int. J. Heat and Mass Transfer, 52 (2009), 232–238 | DOI | Zbl

[18] Yu. M. Matsevityi, S. V. Alekhina, V. T. Borukhov, G. M. Zayats, A. O. Kostikov, “Identifikatsiya koeffitsienta teploprovodnosti dlya kvazistatsionarnykh uravnenii teploprovodnosti”, IFZh, 90:6 (2017), 1364–1370

[19] V. T. Borukhov, G. M. Zayats, The inverse problem of heat conduction in the case of nonuniqueness: a functional identification approach https://ssrn.com/abstract=4060732 | DOI

[20] Yu. G. Evtushenko, V. I. Zubov, “Generalized fast automatic differentiation technique”, J. Comput. Math. Math. Phys., 56:11 (2016), 1819–1833 | DOI | MR | Zbl

[21] V. I. Zubov, “Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation”, J. Comput. Math. Math. Phys., 56:10 (2016), 1743–1757 | DOI | MR | Zbl

[22] A. F. Albu, Y. G. Evtushenko, V. I. Zubov, “Use of second-order optimization methods for solving the inverse coefficient problem in the three-dimensional formulation”, Proc. of IMM Ural Branch of the Russian Academy of Sciences, 27:4 (2021), 19–34 | MR

[23] L. M. Silverman, “Inversion of multivariate linear systems”, Automat. Control, IEEE Trans., 14 (1969), 270–276 | DOI | MR

[24] V. T. Borukhov, “Inversion of distributed linear time-invariant dynamical systems”, Automation and Remote Control, 43 (1982), 593–599 | MR | Zbl

[25] V. T. Borukhov, G. M. Zayats, “Identification of a time-dependent source term in nonlinear hyperbolic or parabolic heat equation”, Int. J. Heat and Mass Transfer, 91 (2015), 1106–1113 | DOI

[26] V. T. Borukhov, P. N. Vabishchevich, “Numerical solution of the inverse problem of reconstructing a distributed right-hand side of a parabolic equation”, Comput. Phys. Commun., 126:1–2 (2000), 32–36 | DOI | MR | Zbl

[27] V. T. Borukhov, V. I. Korzyuk, “Primenenie neklassicheskikh kraevykh zadach dlya vosstanovleniya granichnykh rezhimov protsessov perenosa”, Vestn. Belorus. un-ta. Ser. 1, 2000, no. 3, 54–57 | Zbl

[28] V. T. Borukhov, P. N. Vabischevich, V. I. Korzyuk, “Svedenie odnogo klassa obratnykh zadach teploprovodnosti k pryamym nachalno-kraevym zadacham”, IFZh, 73:4 (2000), 744–747

[29] V. I. Korzyuk, V. T. Borukhov, “Smeshannye zadachi dlya uravneniya teploprovodnosti s integro-differentsialnymi usloviyami na granitse”, Vestn. Belorus. un-ta. Ser. 1, 2002, no. 1, 57–64

[30] V. T. Borukhov, G. M. Zayats, “Identifikatsiya istochnikov protsessov perenosa, opisyvaemykh uravneniyami parabolicheskogo tipa”, Tr. IX Mezhdunar. konf. «Identifikatsiya sistem i zadachi upravleniya», SICPRO'12 (Moskva, 30 yanvarya–2 fevralya 2012 g.), Institut problem upravleniya im. V. A. Trapeznikova RAN, 94–108

[31] V. T. Borukhov, G. M. Zayats, “Vosstanovlenie vkhodnykh signalov dlya odnogo klassa kvazilineinykh sistem giperbolicheskogo tipa”, XII Vserossiiskoe soveschanie po problemam upravleniya VSPU-2014, trudy (Moskva, 16-19 iyunya 2014 g.), IPU RAN, M., 2014, 2777–2786

[32] S. L. Sobolev, “Lokalno-neravnovesnye modeli protsessov perenosa”, Uspekhi fiz. nauk, 167:10 (1997), 1095–1106 | DOI

[33] D. Jou, J. Casas-Vazquez, J. Lebon, Extended Irreversible Thermodynamics, Springer, Berlin, 2010 | MR | Zbl

[34] V. T. Borukhov, G. M. Zayats, Yu. V. Stetsenko, R. V. Konovalov, “Opredelenie koeffitsientov teplootdachi v protsesse zatverdevaniya otlivki v struinom kristallizatore”, IFZh, 85:1 (2012), 181–187

[35] J. V. Beck, B. Blackwell, C. R. St. Clair, Inverse Heat Conduction: Ill-Posed Problems, Wiley, New York, 1985 | MR | Zbl

[36] V. T. Borukhov, O. I. Kostyukova, M. A. Kurdina, “Tracking of the preset program of weighted temperatures and reconstruction of heat transfer coefficients”, J. Eng. Phys. Thermophys., 83:3 (2010), 622–631 | DOI

[37] V. T. Borukhov, O. I. Kostyukova, “Identification of time-dependent coefficients of heat transfer by the method of suboptimal stage-by-stage optimization”, Int. J. Heat and Mass Transfer., 59 (2013), 286–294 | DOI

[38] V. T. Borukhov, O. I. Kostyukova, “Reconstruction of the Surface Heat Flux for a Quasilinear System of the Hyperbolic Type Heat-Conduction Equations”, Communications in Computer and Information Science, 499 (2015), 49–67 | DOI

[39] V. T. Borukhov, O. I. Kostyukova, “Reconstruction of heat transfer coefficients using the approach of stage-by-stage suboptimal optimization and Huber-Tikhonov filtering of input data”, Automatic Control and Computer Sciences, 47:6 (2013), 289–299 | DOI | MR

[40] O. I. Kostyukova, E. A. Kostina, N. M. Fedortsova, “Parametric optimal control problems with weighted $L_1$-norm in the cost function”, Automatic Control and Computer Sciences, 44:4 (2010), 179–190 | DOI

[41] O. I. Kostyukova, E. A. Kostina, N. M. Fedortsova, “Parametricheskie zadachi optimalnogo upravleniya so vzveshennymi $L_1$- i $L_2$-normami v kriterii kachestva”, Tr. In-ta matematiki, 19:2 (2011), 47–59 | Zbl

[42] O. M. Alifanov, Identifikatsiya protsessov teploobmena letatelnykh apparatov (vvedenie v teoriyu obratnykh zadach teploobmena), Mashinostroenie, M., 1979

[43] P. J. Huber, “Robust estimation of a location parameter”, Annals Math. Stat., 35:1 (1964), 73–101 | DOI | MR | Zbl

[44] V. T. Borukhov, “Obratnaya zadacha Shturma-Liuvillya v teorii realizatsii lineinykh dinamicheskikh sistem”, Avtomatika i telemekhanika, 1994, no. 4, 13–21