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Dal'nevostochnyi Matematicheskii Zhurnal, 2010, Volume 10, Number 2, Pages 93–105 (Mi dvmg62)  

This article is cited in 13 scientific papers (total in 13 papers)

Inverse problem of identification of the diffusion coefficient in diffision-reaction equation

I. S. Vakhitov

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
References:
Abstract: The solvability and uniqueness of inverse extremum problem of identification of the diffusion coefficient in a two-dimensional diffusion-reaction equation are proved. The numerical algorithm of solving the inverse problem is developted and realized. The results of numerical experiments are discussed.
Key words: elliptic equation, identification problem, diffusion coefficient, Newton method, uniqueness.
Received: 08.01.2010
Document Type: Article
UDC: 517.95
MSC: 76D55
Language: Russian
Citation: I. S. Vakhitov, “Inverse problem of identification of the diffusion coefficient in diffision-reaction equation”, Dal'nevost. Mat. Zh., 10:2 (2010), 93–105
Citation in format AMSBIB
\Bibitem{Vak10}
\by I.~S.~Vakhitov
\paper Inverse problem of identification of the diffusion coefficient in diffision-reaction equation
\jour Dal'nevost. Mat. Zh.
\yr 2010
\vol 10
\issue 2
\pages 93--105
\mathnet{http://mi.mathnet.ru/dvmg62}
Linking options:
  • https://www.mathnet.ru/eng/dvmg62
  • https://www.mathnet.ru/eng/dvmg/v10/i2/p93
  • This publication is cited in the following 13 articles:
    1. A. V. Chernov, “On the structure of a solution set of controlled initial-boundary value problems”, Russian Math. (Iz. VUZ), 60:2 (2016), 62–71  mathnet  crossref  isi
    2. A. V. Chernov, “O edinstvennosti resheniya obratnoi zadachi opredeleniya parametrov v starshem koeffitsiente i pravoi chasti ellipticheskogo uravneniya”, Dalnevost. matem. zhurn., 16:1 (2016), 96–110  mathnet  elib
    3. R. A. Aliev, “Finding the coefficients of a linear elliptic equation”, J. Appl. Industr. Math., 10:2 (2016), 168–178  mathnet  crossref  crossref  mathscinet  elib
    4. R. A. Aliev, “Ob opredelenii koeffitsientov pri starshikh proizvodnykh v lineinom ellipticheskom uravnenii”, Vladikavk. matem. zhurn., 18:3 (2016), 3–14  mathnet
    5. A. V. Chernov, “On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation”, Comput. Math. Math. Phys., 55:2 (2015), 212–226  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. R. A. Aliev, “Obratnaya zadacha opredeleniya koeffitsienta v ellipticheskom uravnenii”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:2 (2015), 5–13  mathnet  elib
    7. A. V. Chernov, “Ob analoge teoremy Uintnera dlya upravlyaemogo ellipticheskogo uravneniya”, Izv. IMI UdGU, 2015, no. 2(46), 228–235  mathnet  elib
    8. Andrei V. Chernov, “O suschestvovanii ε-ravnovesiya v differentsialnykh igrakh, svyazannykh s ellipticheskimi uravneniyami, upravlyaemymi mnogimi igrokami”, MTIP, 6:1 (2014), 91–115  mathnet
    9. R. A. Aliev, “Ob opredelenii neizvestnykh koeffitsientov pri starshikh proizvodnykh v lineinom ellipticheskom uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(36) (2014), 31–43  mathnet  crossref  zmath  elib
    10. 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  mathnet  crossref  mathscinet
    11. 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  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    12. Aliev Ramiz Atysh ogly, “Teorema edinstvennosti odnoi obratnoi zadachi dlya kvazilineinogo uravneniya ellipticheskogo tipa”, Izvestiya vysshikh uchebnykh zavedenii. severo-kavkazskii region. seriya: estestvennye nauki, 2012, no. 5, 5–10  elib
    13. R. A. Aliev, “Ob opredelenii neizvestnykh koeffitsientov v kvazilineinom ellipticheskom uravnenii”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 5, 4–11  mathnet
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