Karachik Valeriy

University

Federal State Autonomous Educational Institution of Higher Education “South Ural State University (National research university)”

English proficiency

Intermediate

The program of study for which the graduate student will be accepted

Mechanics and mathematics

The code of the direction of study for which the graduate student will be accepted

01.06.01

List of research projects of a potential research supervisor (participation / leadership)

Development of methods for solving boundary value problems with involution

List of possible research topics

  • Construction of Green's functions for problems of Neumann type for the biharmonic equation.
  • Nonlocal problems with involution for the Poisson and Helmholtz equations.
  • Solvability of Neumann-type problems for a polyharmonic equation.

Research supervisor:

Карачик В.В.

Valeriy V. Karachik,

Doctor of Science,

South Ural State University

Headline:

Boundary value problems for a polyharmonic equation with higher order normal derivatives on the boundary.

Supervisor’s research interests:

Partial differential equations, boundary, value problems, polyharmonic equation, nonlocal Dirichlet problem, Neumann-type problems, method of Green Function, polynomial solutions.

Research highlights:

Collaboration with Department of Mathematics, A.Yasawi International Kazakh-Turkish University.

Supervisor’s specific requirements:

  • mathematical analysis, linear algebra,
  • differential equations,
  • equations of mathematical physics.

Supervisor’s main publications:

  • V. Karachik, “Greens function of Dirichlet problem for biharmonic equation in the ball”, Complex Variables and Elliptic Equations, 64:9 (2019), 1500–1521.
  • V. V. Karachik, “Class of Neumann-Type Problems for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 60:1 (2020), 144–162.
  •  V. V. Karachik, B. Kh. Turmetov, “On Green’s function of the Robin problem for the Poisson equation”, Advances in Pure and Applied Mathematics, 10:3 (2019), 203–214.
  • V. V. Karachik, A. M. Sarsenbi, B. Kh. Turmetov, “On the solvability of the main boundary value problems for a nonlocal Poisson equation”, Turkish Journal of Mathematics, 43 (2019), 1604–1625.
  • V. V. Karachik, “Riquier-Neumann Problem for the Polyharmonic Equation in a Ball”, Differential Equations, 54:5 (2018), 648–657.
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