Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
Keywords: partial differential equations, boundary value problems, polynomial solutions, polyharmonic functions, Greens function, special polynomials and functions.
UDC: 517.956.22, 517.956, 517.956.225, 517.572, 517.575
MSC: 35C05, 35C10, 35C11, 35J05, 35J40, 31B30, 11B37

Subject:

Representations of solutions to boundary value problems for partial differential equations: solutions in closed form, series solutions, integral representations of solutions, Green's function.

Main publications:

1. V. V. Karachik, “A problem for the polyharmonic equation in the sphere”, Siberian Mathematical Journal, 32:5 (1991), 767–774    
2. V. V. Karachik, “Polynomial solutions to the systems of partial differential equations with constant coefficients”, Yokohama Math. J., 47 (2000), 121–142  
3. V. V. Karachik, Method of normalized systems of functions, Publishing Center of SUSU, Chelyabinsk, 2014  
4. V. V. Karachik, “Construction of Polynomial Solutions to the Dirichlet Problem for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 54:7 (2014), 1122–1143      
5. V. V. Karachik, “On Green function of the Dirichlet problem for polyharmonic equation in the ball”, Axioms, 12:6 (2023), 543    

Recent publications

Presentations in Math-Net.Ru

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Organisations:

• South Ural State University (National research university)
• University of World Economy and Diplomacy of the Ministry of Foreign Affairs of the Republic of Uzbekistan
• Cybernetics Institute, Academy of Sciences of the RUz