The boundary control problem for a nonlinear convection – diffusion – reaction equation

 
PIIS004446690003558-4-1
DOI10.31857/S004446690003558-4
Publication type Article
Status Published
Authors
Affiliation:
IPM FEB RAS
FEFU
Address: Russian Federation
Affiliation:
Address: Russian Federation
Journal nameZhurnal vychislitelnoi matematiki i matematicheskoi fiziki
EditionVolume 58 Issue 12
Pages2139-2152
Abstract

  

Keywords
AcknowledgmentThe first author was supported by the FANO in the framework of the state assignment (topic number 0263-2018-0001), the second author was supported by the Russian Foundation for Basic Research (project code 16-01-00365-a) and the Far East Far East Academy of Basic Research (project code 18-5-064).
Received23.01.2019
Publication date23.01.2019
Cite   Download pdf To download PDF you should sign in
Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

views: 1066

Readers community rating: votes 0

1. Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnykh zadach. M.: Nauka. 1986.

2. Ito K., Kunish K. Estimation of the convection coefficient in elliptic equations // Inverse Problems. 1997. V. 14. P. 995–1013.

3. Agoshkov V.I., Minuk F.P., Rusakov A.S., Zalesny V.B. Study and solution of identification problems for nonstationary 2D– and 3D–convection–diffusion–reaction // Russ. J. Numer. Anal. Math. Modelling. 2005. V. 20. P. 19–43.

4. Alekseev G.V., Tereshko D.A. On solvability of inverse extremal problems for stationary equations of viscous heat conducting fluid // J. Inv. Ill-Posed Probl. 1998. V. 6, N 6 P. 521–562.

5. Alekseev G.V., Adomavichus E.A. Theoretical analysis of inverse extremal problems of admixture diffusion in viscous fluid // J. Inv. Ill-Posed Probl. 2001. V. 9, N 5. P. 435–468.

6. Alekseev G.V. Razreshimost' ehkstremal'nykh zadach dlya statsionarnykh uravnenij teplomassoperenosa // Sib. mat. zhurn. 2001. T. 42, N 5. S. 971–991.

7. Nguyen P.A., Raymond J.-P. Control problems for convection–diffusion equations with control localized on manifolds // ESAIM: Control, Optimisation and Calculus of Variations. 2001. V. 6. P. 467–488.

8. Nguyen P.A., Raymond J.-P. Pointwise control of the Boussinesq system // Systems Control Lett. 2011. V. 60. P. 249–255.

9. Alekseev G.V. Obratnye ehkstremal'nye zadachi dlya statsionarnykh uravnenij v teorii massoperenosa // Zhurn. vychisl. matem. i matem. fiziki. 2002. T. 42, N 3. S. 380–394.

10. Alekseev G.V., Soboleva O.V., Tereshko D.A. Zadachi identifikatsii dlya statsionarnoj modeli masso-perenosa // Prikl. mekhan. tekhn. fizika. 2008. T. 49, N 4. S. 24–35.

11. Alekseev G.V., Tereshko D.A. Analiz i optimizatsiya v gidrodinamike vyazkoj zhidkosti. Vladivostok.: Dal'nauka. 2008.

12. Alekseev G.V., Vakhitov I.S., Soboleva O.V. Otsenki ustojchivosti v zadachakh identifikatsii dlya uravneniya konvektsii–diffuzii–reaktsii // Zhurn. vychisl. matem. i matem. fiziki. 2012. T. 52, N 12. S. 2190–2205.

13. Penenko V.V. Variatsionnye metody usvoeniya dannykh i obratnye zadachi dlya izucheniya atmosfery, okeana i okruzhayuschej sredy // Sib. zhurn. vychisl. matem. 2009. T. 12. S. 421–434.

14. Dement'eva E.V., Karepova E.D., Shajdurov V.V. Vosstanovlenie granichnoj funktsii po dannym nablyudenij dlya zadachi rasprostraneniya poverkhnostnykh voln v akvatorii s otkrytoj granitsej // Sib. zhurn. industr. matem. 2013. T. 16, N 1. S. 10–20.

15. Korotkij A.I., Kovtunov D.A. Rekonstruktsiya granichnykh rezhimov v obratnoj zadache teplovoj konvektsii vysokovyazkoj zhidkosti // Tr. IMM. 2006. T. 12. S. 88–97.

16. Korotkij A.I., Kovtunov D.A Optimal'noe granichnoe upravlenie sistemoj, opisyvayuschej teplovuyu konvektsiyu // Tr. IMM. 2006. T. 16. S. 76–101.

17. Brizitskij R.V., Saritskaya Zh.Yu. Kraevye i ehkstremal'nye zadachi dlya nelinejnogo uravneniya konvektsii–diffuzii–reaktsii // Sib. ehl. matem. izvestiya. 2015. T. 12. S. 447–456.

18. Alekseev G.V., Brizitskij R.V., Saritskaya Zh.Yu. Otsenki ustojchivosti reshenij ehkstremal'nykh zadach dlya nelinejnogo uravneniya konvektsii–diffuzii–reaktsii // Sib. zhurn. industr. matem. 2016. T. 19, N 2. S. 3–16.

19. Brizitskij R.V., Saritskaya Zh.Yu. Ustojchivost' reshenij ehkstremal'nykh zadach dlya nelinejnogo uravneniya konvektsii–diffuzii–reaktsii pri uslovii Dirikhle // Zhurn. vychisl. matem. i matem. fiziki. 2016. T. 56, N 12. S. 60–71.

20. Brizitskij R.V., Saritskaya Zh.Yu. Ob ustojchivosti reshenij zadach upravleniya dlya uravneniya konvektsii–diffuzii–reaktsii s sil'noj nelinejnost'yu // Differents. uravneniya. 2017. T. 53, N 4. S. 493–504.

21. Brizitskij R.V., Saritskaya Zh.Yu. Koehffitsientnye obratnye zadachi dlya nelinejnogo uravneniya konvektsii–diffuzii–reaktsii // Izvestiya RAN. Ser. matem. 2018. T. 82, vyp. 1. S. 17–33.

22. Kovtanyuk A.E., Chebotarev A.Yu. Statsionarnaya zadacha svobodnoj konvektsii s radiatsionnym teploobmenom // Differents. uravneniya. 2014. T. 50, N 12. S. 1590–1597.

23. Kovtanyuk A.E., Chebotarev A.Yu., Botkin N.D., Hoffmann K.-H. Optimal boundary control of a steady-state heat transfer model accounting for radiative effects // J. Math. Anal. Appl. 2016. V. 439. P. 678–689.

24. Grenkin G.V., Chebotarev A.Yu. Nestatsionarnaya zadacha svobodnoj konvektsii s radiatsionnym teploobmenom // Zhurn. vychisl. matem. i matem. fiziki. 2016. T. 56, N 2. S. 275–282.

25. Fursikov A.V. Optimal'noe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya. Novosibirsk: Nauchnaya kniga. 1999.

26. Alekseev G.V., Romanov V.G. Ob odnom klasse nerasseivayuschikh akusticheskikh obolochek dlya modeli anizotropnoj akustiki // Sib. zhurn. industr. matem. 2011. T. 14, N 2. S. 15–20.

27. Alekseev G.V., Levin V.A. Optimizatsionnyj metod otyskaniya parametrov neodnorodnoj zhidkoj sredy v zadache maskirovki material'nykh tel ot akusticheskoj lokatsii // Dokl. AN. 2014. T. 454, N 4. S. 406–410.

28. Alekseev G.V., Brizitskij R.V. Otsenki ustojchivosti reshenij zadach upravleniya dlya upravnenij Maksvella so smeshannymi granichnymi usloviyami // Differents. uravneniya. 2013. T. 49, N 8. S. 993–1004.

Система Orphus

Loading...
Up