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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 633–647 (Mi smj2351)  

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

An inverse problem for an equation of elliptic-hyperbolic type with a nonlocal boundary condition

K. B. Sabitov, N. V. Martem'yanova

Samara State Academy of Social Sciences and Humanities, Samara

Abstract: We examine a mixed type equation with the Lavrent'ev–Bitsadze operator and an unknown right-hand side in a rectangle and study a nonlocal boundary value problem in which the values of the stream function on the lateral sides of the rectangle are equal. The solution is given as a sum of a biorthogonal series. The uniqueness criterion and stability of solutions with respect to the boundary data are established.

Keywords: mixed type equation, inverse problem, spectral method, uniqueness, existence, stability.

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English version:
Siberian Mathematical Journal, 2012, 53:3, 507–519

Bibliographic databases:

UDC: 517.95
Received: 11.08.2010

Citation: K. B. Sabitov, N. V. Martem'yanova, “An inverse problem for an equation of elliptic-hyperbolic type with a nonlocal boundary condition”, Sibirsk. Mat. Zh., 53:3 (2012), 633–647; Siberian Math. J., 53:3 (2012), 507–519

Citation in format AMSBIB
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\paper An inverse problem for an equation of elliptic-hyperbolic type with a~nonlocal boundary condition
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 3
\pages 633--647
\mathnet{http://mi.mathnet.ru/smj2351}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978580}
\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 3
\pages 507--519
\crossref{https://doi.org/10.1134/S0037446612020310}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. B. Sabitov, G. Yu. Udalova, “Kraevaya zadacha dlya uravneniya smeshannogo tipa tretego poryadka s usloviyami periodichnosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(32) (2013), 29–45  mathnet  crossref  zmath
    2. T. K. Yuldashev, “Dvoinaya obratnaya zadacha dlya integro-differentsialnogo uravneniya Fredgolma ellipticheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(35) (2014), 39–49  mathnet  crossref  zmath
    3. G. Oralsyn, M. A. Sadybekov, “An inverse coefficient problem of heat conductivity with a nonlocal Samarskii–Ionkin type condition”, Advancements in Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, UNSP 020016  crossref  isi  scopus
    4. I. Orazov, M. A. Sadybekov, “On an inverse problem of mathematical modeling of the extraction process of polydisperse porous materials”, Advancements in Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, UNSP 020005  crossref  isi  scopus
    5. A. U. Sazaklioglu, A. S. Erdogan, “On the unique solvability of an inverse problem for a semilinear parabolic equation”, Advancements in Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020050  crossref  isi  scopus
    6. I. Orazov, M. A. Sadybekov, “One-dimensional diffusion problem with not strengthened regular boundary conditions”, 41st International Conference Applications of Mathematics in Engineering and Economics (AMEE'15), AIP Conf. Proc., 1690, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2015, UNSP 040007  crossref  isi  scopus
    7. T. K. Yuldashev, “Inverse problem for a nonlinear Benney–Luke type integro-differential equations with degenerate kernel”, Russian Math. (Iz. VUZ), 60:9 (2016), 53–60  mathnet  crossref  isi
    8. T. K. Yuldashev, “Obratnaya zadacha dlya integro-differentsialnogo uravneniya Fredgolma tretego poryadka s vyrozhdennym yadrom”, Vladikavk. matem. zhurn., 18:2 (2016), 76–85  mathnet
    9. N. E. Erzhanov, I. Orazov, “On one mathematical model of the extraction process of polydisperse porous material”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:2 (2016), 5–15  mathnet  crossref  elib
    10. D. Suragan, G. Oralsyn, “Inverse coefficient problems for mathematical models of one-dimensional heat transfer with a generalized condition of preservation of medium temperature”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040017  crossref  isi  scopus
    11. A. I. Grigoreva, “Zadacha sopryazheniya dlya psevdoparabolicheskikh i psevdogiperbolicheskikh uravnenii”, Matematicheskie zametki SVFU, 23:3 (2016), 27–45  mathnet  elib
    12. K. B. Sabitov, N. V. Martem'yanova, “Inverse problem for Lavrent'ev–Bitsadze equation connected with the search of elements in right-hand side”, Russian Math. (Iz. VUZ), 61:2 (2017), 36–48  mathnet  crossref  isi
    13. K. B. Sabitov, N. V. Martemyanova, “K voprosu o korrektnosti obratnykh zadach dlya neodnorodnogo uravneniya Gelmgoltsa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:2 (2018), 269–292  mathnet  crossref  zmath  elib
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