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Sibirsk. Mat. Zh., 2013, Volume 54, Number 6, Pages 1287–1293 (Mi smj2495)  

This article is cited in 31 scientific papers (total in 31 papers)

On a nonlocal boundary value problem for the multidimensional heat equation in a noncylindrical domain

T. Sh. Kal'menov, N. E. Tokmagambetov

Institute of Mathematics and Mathematical Modelling, Ministry of Education and Science of the Republic of Kazakhstan, Almaty, Kazakhstan

Abstract: We study a nonlocal initial-boundary value problem for the space-multidimensional heat equation in a noncylindrical domain. It is proven that the heat potential is a unique classical solution to this problem.

Keywords: multidimensional heat equation, nonlocal boundary value problem, heat potential, noncylindrical domain.

Full text: PDF file (260 kB)
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English version:
Siberian Mathematical Journal, 2013, 54:6, 1023–1028

Bibliographic databases:

UDC: 517.95
Received: 05.12.2012
Revised: 09.04.2013

Citation: T. Sh. Kal'menov, N. E. Tokmagambetov, “On a nonlocal boundary value problem for the multidimensional heat equation in a noncylindrical domain”, Sibirsk. Mat. Zh., 54:6 (2013), 1287–1293; Siberian Math. J., 54:6 (2013), 1023–1028

Citation in format AMSBIB
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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. N. E. Tokmagambetov, “Gellerstedt Equation with the Perturbation of the Cauchy Condition”, J. Math. Sci., 213:6 (2016), 910–916  mathnet  crossref
    2. T. Sh. Kal'menov, D. Suragan, “On permeable potential boundary conditions for the Laplace–Beltrami operator”, Siberian Math. J., 56:6 (2015), 1060–1064  mathnet  crossref  crossref  mathscinet  isi  elib
    3. M. M. Amangaliyeva, M. T. Jenaliyev, M. T. Kosmakova, M. I. Ramazanov, “Uniqueness and non-uniqueness of solutions of the boundary value problems of the heat equation”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, ed. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020028  crossref  isi  scopus
    4. T. Sh. Kal'menov, G. D. Arepova, “On a boundary condition of the surface heat potential”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020054  crossref  isi  scopus
    5. T. Sh. Kal'menov, M. Otelbaev, “Criterion of boundary integral operator”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, ed. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020002  crossref  isi  scopus
    6. B. Kanguzhin, N. Tokmagambetov, N. Bekbayev, “The Green function and correctly solvable non-local boundary value problems for the polyharmonic equation in a punctured domain”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020101  crossref  mathscinet  isi  scopus
    7. B. D. Koshanov, M. D. Koshanova, “On the representation of the Green function of the Dirichlet problem and their properties for the polyharmonic equations”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, ed. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020020  crossref  isi  scopus
    8. 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, ed. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, UNSP 020016  crossref  isi  scopus
    9. I. Orazov, A. Shaldanbayev, M. Shomanbayeva, “Solution of a singularly perturbed Cauchy problem using a method of a deviating argument”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, ed. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020072  crossref  isi  scopus
    10. 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, ed. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, UNSP 020005  crossref  isi  scopus
    11. M. A. Sadybekov, B. T. Torebek, “On a new class of nonlocal problems for the Laplace operator”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020073  crossref  isi  scopus
    12. N. Tokmagambetov, G. Nalzhupbayeva, “Operator perturbed Cauchy problem for the Gellerstedt equation”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020098  crossref  isi  scopus
    13. 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, ed. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2015, UNSP 040007  crossref  isi  scopus
    14. T. Sh. Kal'menov, M. Otelbaev, “Boundary criterion for integral operators”, Dokl. Math., 93:1 (2016), 58–61  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    15. 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
    16. T. Sh. Kal'menov, G. D. Arepova, “On a heat and mass transfer model for the locally inhomogeneous initial data”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:2 (2016), 124–129  mathnet  crossref  elib
    17. T. Sh. Kal'menov, G. D. Arepova, “Quasi-spectral decomposition of the heat potential”, Electron. J. Differ. Equ., 2016, 76  mathscinet  zmath  isi
    18. T. Kal'menov, G. Arepova, “On a heat and mass transfer model for the locally inhomogeneous initial data”, 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 040028  crossref  isi  scopus
    19. M. Sadybekov, B. Torebek, “On a class of nonlocal boundary value problems for the Laplace operator in a disk”, 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 040025  crossref  isi  scopus
    20. A. A. Sarsenbi, L. K. Zhumanova, “First regularized trace of integro-differential Sturm–Liouville operator on a segment with punctured points at generalized conditions of bonding in deleted points”, 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 040009  crossref  isi  scopus
    21. G. Arepova, “On a regular problem for an elliptic-parabolic equation with a potential boundary condition”, International Conference On Analysis And Applied Mathematics (ICAAM 2016), AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020041  crossref  isi  scopus
    22. T. Sh. Kalmenov, G. D. Arepova, “On a heat transfer model for a locally inhomogeneous initial data”, International Conference On Analysis And Applied Mathematics (ICAAM 2016), AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020026  crossref  isi  scopus
    23. B. Kanguzhin, G. Nalzhupbayeva, “On identities for eigenvalues of a well-posed perturbation of the Laplace operator in a punctured domain”, International Conference On Analysis And Applied Mathematics (ICAAM 2016), AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020092  crossref  isi  scopus
    24. A. Tengayeva, G. Dildabek, “Existence of eigenvalues of problem with shift for an equation of parabolic-hyperbolic type”, International Conference On Analysis And Applied Mathematics (ICAAM 2016), AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020146  crossref  isi  scopus
    25. T. Sh. Kal'menov, “Boundary conditions for the Cauchy potential for two-dimensional hyperbolic equations”, International Conference Functional Analysis In Interdisciplinary Applications (FAIA 2017), AIP Conf. Proc., 1880, ed. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 040002  crossref  isi  scopus
    26. T. Sh. Kal'menov, M. A. Sadybekov, “On a Frankl-type problem for a mixed parabolic-hyperbolic equation”, Siberian Math. J., 58:2 (2017), 227–231  mathnet  crossref  crossref  isi  elib  elib
    27. T. Sh. Kal'menov, G. D. Arepova, D. D. Arepova, “Boundary condition of the volume potential for an elliptic-parabolic equation with a scalar parameter”, Electron. J. Differ. Equ., 2018  mathscinet  isi
    28. Sh. K. T., M. Otelbaev, G. D. Arepova, “Bitsadze–Samarskii boundary condition for elliptic-parabolic volume potential”, Dokl. Math., 97:3 (2018), 223–226  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
    29. M. Sadybekov, G. Oralsyn, “On trace formulae of the generalised heat potential operator”, J. Pseudo-Differ. Oper. Appl., 9:1 (2018), 143–150  crossref  mathscinet  zmath  isi  scopus
    30. T. Sh. Kal'menov, G. D. Arepova, “A criterion for the existence of soliton solutions of telegraph equation”, Bull. Karaganda Univ-Math., 91:3 (2018), 45–52  crossref  isi
    31. T. Kal'menov, G. D. Arepova, “On a boundary condition of Bitsadze-Samarskii for the Lavrent'ev-Bitsadze equation”, International Conference on Analysis and Applied Mathematics (ICAAM 2018), AIP Conf. Proc., 1997, eds. A. Ashyralyev, A. Lukashov, M. Sadybekov, Amer. Inst. Phys., 2018, 020002-1  crossref  isi  scopus
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