Research interests:
My area of specialization is related to evolutionary partial differential equations and non-Newtonian hydrodynamics. In particular, my interest is focused on the study of existence, uniqueness, and the qualitative properties (blow up and large time behavior) of solutions of direct and inverse problems for Kelvin-Voigt equations for homogeneous and nonhomogeneous fluids, linear and nonlinear pseudo-parabolic equations with p-Laplacian.

List of Publications:
Researchgate link: https://www.researchgate.net/profile/Khonatbek-Khompysh

1. ARTICLES
3. Khompysh Kh. Blow-up phenomena for generalized pseudoparabolic equation with
   variable exponents and coefficients//Applicable Analysis, 2023, 102(6), pp 1786–1797
   https://doi.org/10.1080/00036811.2021.2003342 (WoS, Scopus)
4. Antontsev S.N. Khompysh Kh., Inverse problems for a Boussinesq system for
   incompressible viscoelastic fluids//Mathematical Methods in the Applied
   Sciences, 2023, 2023, 46(9), pp. 11130–11156.
   https://doi.org/10.1002/mma.9172 (WoS, Scopus)
5. Khompysh Kh. Nugymanova, N.K. Inverse problem for integro-differential KelvinVoigt equations //Journal of Inverse and Ill-Posed Problems, 2022,
   DOI: 10.1515/jiip-2020-0157 In press (WoS, Scopus)
6. Khompysh Kh., A.Kabidoldanova, An initial-boundary value problem for KelvinVoigt equations with
   (p(x),q(x),m(x))
   structure // International journal of
   mathematics and physics, 13(1) 2022, 41-47 DOI:
   https://doi.org/10.26577/ijmph.2022.v13.i1.04 (WoS, Scopus)
7. Khompysh Kh., A. Shakir, A.Kabidoldanova, Solvability of a nonlinear inverse
   problem for a pseudoparabolic equation with p-Laplacian//Journal of Mathematics,
   Mechanics and Computer Science (Вестник КазНУ им. Аль-Фараби, Серия
   математика, механика, информатика) №2 (110) 2021, 35-46.
   DOI:https://doi.org/10.26577/JMMCS.2021.v110.i2.04 (WoS)
8. Antontsev S.N. and H.B. de Oliveira, Khompysh Kh. Kelvin-Voigt equations for
   incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and
   damping// Nonlinear Differ. Equ. Appl. 29, 60 (2022). https://doi.org/10.1007/s00030-
   022-00794-z (WoS, Scopus)
9. Khompysh Kh., Kenzhebai Kh., An inverse problem for Kelvin–Voigt equations
   perturbed by isotropic diffusion and damping//Mathematical Methods in Applied
   Sciences, 2022, 45(7), pp. 3817–3842, https://doi.org/10.1002/mma.8018 (WoS,
   Scopus)
10. S.N. Antontsev, Khompysh Kh., An inverse problem for generalized Kelvin–Voigt
    equation with p-Laplacian and damping term// Inverse Problems, 37(8), 085012
    https://doi.org/10.1088/1361-6420/ac1362 (WoS, Scopus)
11. S.N. Antontsev and H.B. de Oliveira, Khompysh Kh., The classical Kelvin–Voigt
    problem for incompressible fluids with unknown non-constant density: existence,
    uniqueness and regularity//Nonlinearity 34 (2021) 3083–3111
    https://doi.org/10.1088/1361-6544/abe51e (WoS, Scopus)
12. S.N.Antontsev and H.B. de Oliveira, Khompysh Kh. Kelvin-Voigt equations with
    anisotropic relaxation, diffusion and damping: blow up and large time behavior//
    Asymptotic Analysis, vol. 121, no. 2, pp. 125-157, 2021.
    https://dx.doi.org/10.3233/ASY-201597. (WoS, Scopus)
13. S.N. Antontsev and H.B. de Oliveira, Khompysh Kh. Generalized Kelvin-Voigt
    equations for nonhomogeneous and incompressible fluids// COMMUN. MATH. SCI. c
    2019 Vol. 17, No. 7, pp. 1915–1948,
    DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n7.a7 (Q1).
14. S.N. Antontsev and H.B. de Oliveira, Khompysh Kh. Existence and large time
    behavior for generalized Kelvin-Voigt equations governing nonhomogeneous and
    incompressible fluids//2019 J. Phys.: Conf. Ser. 1268 012008. doi:10.1088/1742-
    6596/1268/1/012008
15. S.N. Antontsev and H.B. de Oliveira, Khompysh Kh. Kelvin–Voigt equations
    perturbed by anisotropic relaxation, diffusion and damping//J. Math. Anal. Appl. 473
    (2019) 1122–1154, Thomson Reuters, IF=1.138,
    https://doi.org/10.1016/j.jmaa.2019.01.011
16. Antontsev S.N., Khompysh Kh. Generalized Kelvin-Voigt equations with p-Laplacian
    and source/absorption terms//J. Math. Anal. Appl. 456 (2017) 99–116. Thomson
    Reuters, IF=1,138, https://doi.org/10.1016/j.jmaa.2017.06.056
17. Antontsev S.N., Khompysh Kh. Kelvin–Voight equation with p-Laplacian and
    damping term: Existence, uniqueness and blow-up//J. Math. Anal. Appl. 446 (2017)
    1255–1273. http://dx.doi.org/10.1016/j.jmaa.2016.09.023 Thomson Reuters,
    IF=1,138).
18. Khompysh Kh., Identification of right hand side nonlinear Kelvin-Voigt equations//
    Vestnik KazNPU after Abay, 4(54), 2016. pp. 123-131. (in Russian)
19. Abylkairov U. U., Khompysh Kh. An inverse problem of identifying the coefficient in
    Kelvin-Voight equations// Applied Mathematical Sciences, Journal for Theory and
    applications, Vol. 9, 2015, no. 101-104. -P. 5079-5089. Hicari Ltd, http://www.m-hikari.com
    http://dx.doi.org/10.12988/ams.2015.57464, Scopus.
20. Abylkairov U. U., Mukhambetzhanov S. T., Khompysh Kh. On the ε-approximation
    for the modified equations of the heat convection //Universal Journal of Mathematics
    and Mathematical Sciences © 2014 Pushpa Publishing House, Allahabad, India
    http://pphmj.com/journals/ujmms.htm V.5, N. 1, 2014, P. 37-51.
21. Abylkairov U.U., Khompysh Kh., Sakhaev Sh. On a system of equations with a small
    parameter arising in the numerical analysis of the equations of thermal convection for
    non-Newtonian fluids. // Scientific journal. Joint issue BULLETIN OF THE VKGU
    after D. Serikbaev and Computing Technologies of the Institute of Computational
    Technologies of the Siberian Branch of the Russian Academy of Sciences. UstKamenogorsk city, 2013 P.5. Pp. 76-79. (in Russian)
22. Abylkairov U.U. Khompysh Kh. Classical Unique Solvability of the Quasistationary
    Problem of Heat Convection // scientific journal. Joint issue BULLETIN OF THE
    VKGU after D. Serikbaev and Computing Technologies of the Institute of
    Computational Technologies of the Siberian Branch of the Russian Academy of
    Sciences. Ust-Kamenogorsk city, 2013 P.5. Pp. 70-76. (in Russian)
23. Khompysh Kh. On the Rate of Convergence of Solutions of One
    ε –regularized Problem of Heat Convection for the Kelvin-Voight Fuids// The Bulletin of KazNU,
    Series of Mathematics, Mechanics and Informatics. Almaty, 2012. №1(72) 2012. pp.
    79-86. (in Russian).
24. Khompysh Kh. An ε -approximation and its convergence rate of equation of heat
    convection for Kelvin-Voigt fluids//Vestnik ENU after L.Gumilev, №4(89) 2012, pp.
    42-47. (in Kazakh).
25. Khompysh Kh., Sakhaev Sh. On Stability of the Solutions of the One Nonlinear Value
    Problem of Magnetohydrodynamics// Vestnik KazNPU after Abay. Series of PhysicalMathematical Sciences, №1(21), pp.226-231. Almaty 2008. (in Russian).
26. Khompysh Kh. An Initial-Boundary Value Problem with Free Surface Condition for
    the Modified Heat Convection and it’s ε -Approximations // Vestnik of Al-Farabi
    KazNU, Series of Mathematics, Mechanics and Informatics. Almaty, 2008, №2(57),
    pp. 36-41. (in Russian).
27. CONFERENCE PROCEEDINGS
28. Khompysh Kh., Sharypkhan S. Sakhaev Solvability one of stationary problem of
    magnetohydrodynamics // International Conference on Analysis and Applied
    Mathematics (ICAAM 2016) AIP Conf. Proc. 1759, 020096-1–020096-5;
    http://dx.doi:10.1063/1.4959710/ Proceedings conf. (Индек. в Thomson Reuters).
29. Abylkairov U. U., Khompysh Kh. ε-approximation of the equations of heat convection
    for the Kelvin-Voight fluids//AIP Conference Proceedings 1676, 020059 (2015); doi:
    10.1063/1.4930485 View online: http://dx.doi.org/10.1063/1.4930485
    (индексируемые в Thomson Routers)
30. Khompysh Kh., Sakhaev Sh.S. On estimates of solutions of the linear stationary
    problem of magnetohydrodynamics problem in Sobolev spaces//AIP Conference
    Proceedings 1676, 020033 (2015); doi: 10.1063/1.4930459 View online:
    http://dx.doi.org/10.1063/1.4930459 (индексируемые в Thomson Routers)
31. Abylkairov U. U., Khompysh Kh., Zhensykbaev K.S. Solvability of the initialboundary value problem for Stokes equation inhomogeneous fluids//Transactions of
    the International Scientific Conference «Modern Problems of Applied Mathematics and
    Information Technologies –al-Khorezmiy 2014», V. №1, 15-17 september 2014,
    Samarqant, Uzbekistan, -P. 184-185.
32. Khompysh Kh., Sakhaev Sh. Solution of the of conjugate problem of electrodynamics
    // Proceedings of the international scientific conference “Actual problems of applied
    mathematics and information technologies-al-Khorezmi 2014″, T. №1, September 15-
    17, 2014, Samarkant, Uzbekistan, -S. 140-144. (in Russian)
33. Khompysh Kh. Inverse Problem with Integral Overdetermination for System of
    Equations of Kelvin-Voight Fluids //Advanced Materials Research Vol. 705 (2013) pp
    15-20. © (2013) Trans Tech Publications, Switzerland.
    doi:10.4028/www.scientific.net/AMR.705.15
34. Aitzhanov S.E., Nurbaeva D.M., Ilesova A.N., Khompysh Kh., Tashkenbaeva A.U.,
    Sherniazova K. An Inverse Problem for Linear Navier-Stokes Equations with Integral
    Overdetermination// Materials of V-th International Scientific Methodological
    Conference «Mathematical Modeling and Information Technologies in Education and
    Science» Almaty 2010. V. 1. pp. 12-18. (in Kazakh)
35. Aitzhanov S.E., Bolatuky B., Markhaba K., Toganbai A.S., Khompysh Kh.,
    Khumarbek E. Solvability of the Inverse Problem for Non-Stationary System of
    Magnetohydrodynamics//Materials of Vth International Scientific Methodological
    Conference «Mathematical Modeling and Information Technologies in Education and
    Science» Almaty 2010. V. 1. pp. 6-12. (in Kazakh)
36. Abylkairov U.U. Khompysh Kh., Extremal problem for Navier-Stokes
    system//ABSTRACTS of the third congress of the world mathematical society of
    Turkic countries. Almaty June 30- July -4 2009, vol.1, P. 154.
37. Khompysh Kh., Sakhaev Sh. Solvability Global in Time of the Initial-Boundary Value
    Problem with Free Surface Condition for the Modified Heat Convection // Transactions
    of the International Scientific Conference «Modern Problems of Applied Mathematics
    and Information Technologies –al-Khorezmiy 2009», V. №1, pp. 114-118. Tashkent,
    Uzbekistan, pp. 184-185. (Russian).
    ABSTRACTS
38. Antontsev S.N., Khompysh Kh. Kelvin-Voight equations with p-Laplacian:
    Extinction and blow up //Abstracts of the International Conference Lavrentyev
    readings on mathematics, mechanics and physics devoted to the 115th anniversary of
    Academician MALavrentiev, September 7-11, 2015. Novosibirsk, 2015. -pp. 14-15
39. Antontsev S.N., Khompysh Kh. Kelvin-Voight equations with p-Laplacian:
    Existence, uniqueness, asymptotic behavior and blow up// Abstracts Russian-French
    Workshop “Mathematical Hydrodynamics”, August 22–27, 2016 Novosibirsk, Russia.
    P. 9.
40. Khompysh Kh. An inverse problem for one dimensional Pseudoparabolic
    Equation//The 4 rd Abu Dhabi University Annual International Conference
    Mathematical Sciences and its Applications, Abstracts book, December 27-30, 2015.
41. Abylkairov U.U., Khompysh Kh., The inverse problem for Kelvin-Voigt equations //
    International scientific conference “Actual problems of mathematics and mathematical
    modeling” is dedicated to the 50th anniversary of the establishment of the Institute of
    Mathematics and Mechanics of the Academy of Sciences of the Kazakh SSR, Almaty
    June 1-5, 2015 Abstracts -pp. 219-221, (in Russian)
42. Abylkairov U. U., Mukhambetzhanov S. T., Khompysh Kh., Blow-up of Solutions of
    a One dimensional Pseudoparabolic Equation//The 3 rd Abu Dhabi University Annual
    International Conference Mathematical Sciences and its Applications, Abstracts book,
    December 27-30, 2014. P. 46
43. Abylkairov U.U., S.E.Aitzhanov, Khompysh Kh. Unique Solvability of the Inverse
    Problem Unique solvability of the inverse flow problem for Navier-Stokes equation.
    // Proceedings of the International Scientific and Practical Conference “Theory of
    Functions, Functional Analysis and their Applications” dedicated to the 90th
    anniversary of the Corresponding Member. AN KazSSR, Professor T.I. Amanov.
    Semey, Kazakhstan, October 3-5, 2013. -T.1. -P. 236-237. (in Russian)
44. Abylkairov U. U. Khompysh Kh. Inverse Problem for the Equations of Motion of the
    Kelvin–Voight Fluids//Abstracts of the International Conference «Inverse and ill-posed
    problems of mathematical physics» dedicated to the 80th anniversary of the birthday of
    Academician Mikhail Mikhailovich Lavrent’ev Novosibirsk, Russia, 5–12 August
    2012, -P. 61.
45. Abylkairov U.U., Khompysh Kh., Sakhaev S.Sh. On a Global Solvability One of the
    Initial-Boundary Value Problem of Heat Convections for the Kelvin-Voight
    Fluids//ABSTRACTS of the 4-th congress of the Turkic word mathematical society.
    Baku, Azerbaijan. July 2011. P. 142
    BOOKS, TEXTBOOKS:
46. Khompysh Kh., Sakhaev Sh. Special Functions and Their Applications, Almaty, 2012.
    Kazakh University. P. 124 Textbook. (in Kazakh).
47. Khompysh Kh. Equations of Mathematical Physics, Almaty, 2017. Kazakh
    University. P. 124 Textbook. (in Kazakh).
48. Khompysh Kh. Equations of Mathematical Physics: Theory, exercisesб and individual
    tasks, Almaty, 2018. Kazakh University. P. 293 Textbook. (in Kazakh).
49. Khompysh Kh. And Zhapsarbaeva L.K. Equations of Mathematical Physics,
    Almaty, 2020. Kazakh University. P. 303 Textbook. (in English).