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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 8, Pages 1365–1377 (Mi zvmmf265)  

This article is cited in 14 scientific papers (total in 14 papers)

Source and coefficient inverse problems for an elliptic equation in a rectangle

V. V. Solov'ëv

Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: The inverse problems of determining the source and coefficient of an elliptic equation in a rectangle are studied. Additional information on the solution to the direct problem (overdetermination) is the trace of its solution on an interval inside the rectangle. Sufficient existence and uniqueness conditions (global) are derived for the inverse problems. The study is performed in the class of continuously differentiable functions whose derivatives satisfy a Hölder condition.

Key words: inverse problems, elliptic equation.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:8, 1310–1322

Bibliographic databases:

UDC: 519.633.9
Received: 17.12.2006
Revised: 26.12.2006

Citation: V. V. Solov'ëv, “Source and coefficient inverse problems for an elliptic equation in a rectangle”, Zh. Vychisl. Mat. Mat. Fiz., 47:8 (2007), 1365–1377; Comput. Math. Math. Phys., 47:8 (2007), 1310–1322

Citation in format AMSBIB
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\by V.~V.~Solov'\"ev
\paper Source and coefficient inverse problems for an elliptic equation in a~rectangle
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 8
\pages 1365--1377
\mathnet{http://mi.mathnet.ru/zvmmf265}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2378182}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 8
\pages 1310--1322
\crossref{https://doi.org/10.1134/S096554250708009X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548411765}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Solov'ev, “Coefficient inverse problem for PoissonТs equation in a cylinder”, Comput. Math. Math. Phys., 51:10 (2011), 1738–1745  mathnet  crossref  mathscinet  isi
    2. Aliev Ramiz Atash ogly, “Ob opredelenii neizvestnykh koeffitsientov v kvazilineinom ellipticheskom uravnenii”, Vestn. Yuzhno-Uralskogo gos. un-ta. Ser. Matematika. Mekhanika. Fizika, 2011, no. 32, 4–11  elib
    3. 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
    4. Aliev Ramiz Atash ogly, “Teorema edinstvennosti odnoi obratnoi zadachi dlya kvazilineinogo uravneniya ellipticheskogo tipa”, Izv. vuzov. Severo-kavkazskii region. Ser. Estestvennye nauki, 2012, no. 5, 5–10  elib
    5. Solov'ev V.V., “Inverse Coefficient Problems for Elliptic Equations in a Cylinder: I”, Differ. Equ., 49:8 (2013), 996–1005  crossref  mathscinet  zmath  isi  scopus
    6. 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
    7. Mehraliyev Ya.T., Kanca F., “An Inverse Boundary Value Problem For a Second Order Elliptic Equation in a Rectangle”, Math. Model. Anal., 19:2 (2014), 241–256  crossref  mathscinet  isi  elib  scopus
    8. 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
    9. Ashyralyyev Ch., Dedeturk M., “Approximation of the Inverse Elliptic Problem With Mixed Boundary Value Conditions and Overdetermination”, Bound. Value Probl., 2015, 51  crossref  mathscinet  zmath  isi  elib  scopus
    10. Ashyralyyev Ch., Akkan Ya., “Numerical Solution To Inverse Elliptic Problem With Neumann Type Overdetermination and Mixed Boundary Conditions”, Electron. J. Differ. Equ., 2015, 188  mathscinet  zmath  isi  elib
    11. 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
    12. R. A. Aliev, “Ob opredelenii koeffitsientov pri starshikh proizvodnykh v lineinom ellipticheskom uravnenii”, Vladikavk. matem. zhurn., 18:3 (2016), 3–14  mathnet
    13. Kanca F., “Inverse coefficient problem for a second-order elliptic equation with nonlocal boundary conditions”, Math. Meth. Appl. Sci., 39:11 (2016), 3152–3158  crossref  mathscinet  zmath  isi  elib  scopus
    14. S. B. Sorokin, “An economical algorithm for numerical solution of the problem of identifying the right-hand side of the Poisson equation”, J. Appl. Industr. Math., 12:2 (2018), 362–368  mathnet  crossref  crossref  elib  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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