LEADING SPECIALIST IN INTERNAL AND BOUNDARY CONDITIONS FOR ELLIPTIC EQUATIONS

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CONNECTION

 

ACHIEVEMENTS, AWARDS

 

14 of his/her scientific articles are indexed in SCOPUS and Web of Science databases, with an h-index of 5.

ISHANKULOV TOLIB

Doctor of Physical and Mathematical Sciences, Professor of the Department of Differential Equations

 

Research area:

 

Internal and boundary continuation problems for elliptic equations

Main results of the research:

The problem of continuation of mmm-analytic functions in a polycilindrical domain according to the boundary values of the function and its derivatives up to (m−1)(m-1)(m−1)-th order has been checked for conditional correctness. A theorem on the uniqueness of the solution to this continuation problem has been proven. A theorem about two constants for mmm-analytic functions in a polycilindrical domain has been proved. The Cauchy integral formula and the Carleman formulas for such functions have been established. The problem of continuation for mmm-analytic functions in spherical domains has also been checked for conditional correctness. The Martinelli-Boxner integral formula and the Carleman formulas for such functions have been established. The problem of continuation of the solution of the linear stationary Navier-Stokes system according to the values on the boundary of the regularity domain of the solution and the stress tensor has been checked for conditional correctness. The Carleman formula for the solution of this Cauchy problem has been established. Using the Carleman formula, the stability estimate and regularization of the solution have been obtained. The Carleman formula for a system of first-order linear elliptic type equations with variable coefficients in the plane has been proved. The stability estimate for the solution of the Cauchy problem has been obtained. In the case of polycilindrical domains, minimal uniqueness sets have been found for the continuation problem of pluriharmonic functions according to their boundary values.

Main scientific publications:

 
  • Ishankulov T., Mannonov M. "Continuation of the solution of the inhomogeneous polyanalytic equation" // AIP Conf. Proc. 3147, 020010 (2024) http://doi.org/10.1063/5.0210315.
  • Ishankulov T., Ishankulov F. "On the continuation of the solution of the linearized stationary Navier-Stokes system." Differential Equations, 2021, vol. 57, no. 9, pp. 1153–1163.
  • Ishankulov T., Fozilov D. "Continuation of polyanalytic functions." Izvestiya VUZ. Mathematics, 2021, No. 8, pp. 37–45.
  • Ishankulov T., Fozilov D., Umarov S. "Continuation of the solution of the Cauchy-Riemann inhomogeneous equation." Journal of Critical Reviews, ISSN-2394-5125, Vol. 7, Issue 16, 2020.
  • Ishankulov T. "On the possibility of generalized-analytic continuation to a domain for functions defined on a part of its boundary." Siberian Mathematical Journal, 2000, vol. 41, no. 6, pp. 1350–1356.
  • Ishankulov T., Makhmudov O. "The Cauchy problem for a system of thermoelasticity equations in space." Izvestiya VUZ. Mathematics, 1999, No. 6 (445), pp. 27–32.
  • Ishankulov T., Makhmudov O. "The Cauchy problem for a system of thermoelasticity equations in space." Mathematical Notes, 1998, vol. 64, no. 2, pp. 212–217.
  • Ishankulov T. "On the Cauchy problem for the linear stationary Navier-Stokes system." Siberian Mathematical Journal, 1997, vol. 38, no. 5, pp. 1089–1097.
  • Yarmukhamedov Sh., Ishankulov T., Makhmudov O. "The Cauchy problem for a system of elasticity theory equations in space." Siberian Mathematical Journal, 1992, vol. 33, no. 1, pp. 186–190.
  • Ishankulov T. "On two problems of analytic continuation for functions of several variables." Siberian Mathematical Journal, 1984, vol. 25, no. 3, pp. 89–94.
  • Ishankulov T. "On a problem of analytic continuation for functions of several complex variables." Collection: Non-classical Problems of Mathematical Physics, Novosibirsk, 1981.
  • Ishankulov T. "On a problem of analytic continuation for pluriharmonic functions." Collection: Investigations of the Correctness of Inverse Problems, Novosibirsk, 1981, pp. 84–92.
  • Ishankulov T. "A problem of analytic continuation for generalized-analytic functions." Collection: Investigations of the Correctness of Inverse Problems, Novosibirsk, 1981, pp. 37–43.
  • Ishankulov T. "A problem of analytic continuation for a function of two complex variables." Collection: Ill-posed Mathematical Problems, Novosibirsk, 1979, pp. 71–76.