IRN АР09058677 «Studying the correctness of boundary value problems for nonclassical equations of mathematical physics»

Goal of the project. As a result of the project, properties of the hypergeometric functions of four variables will be studied, relevant relationships will be found, and formulas for the expansion will be derived. Also, with the help of fundamental solutions, well-known boundary-value problems on a finite and infinite domain for a degenerate elliptic equation in four variables will be solved. Sufficient conditions will be obtained for the existence of a unique solution to the first mixed problem for the equation of porous media in the dissipative case in the class of doubly continuous functions. The solution of the problem will be reduced to the solution of the equivalent Volterra equation of the second kind. Solvability and uniqueness of the Cauchy problem, initial-boundary value problems and nonlocal problems with integral conditions will be proved for a partial differential equation of third-order hyperbolic type. Previously unexplored boundary value problems will be solved for a mixed parabolic-hyperbolic equation with a fractional differentiation operator.

 Expected results.

  1. Boundary value problems will be investigated and methods for constructing their solutions for four-dimensional degenerate equations of elliptic type will be developed.
  2. Methods for solving local problems for a hyperbolic equation with memory will be developed.
  3. We will study the question of solvability of local and nonlocal problems for a partial differential equation of hyperbolic type with memory.
  4. We will investigate solutions to boundary value problems in the characteristic triangle for a third-order hyperbolic equation.
  5. We will study the solvability and properties of boundary value problems with an integral conjugation condition for mixed parabolic-hyperbolic equations of the third order.
  6. We will study the solvability of boundary value problems for a mixed parabolic-hyperbolic equation with a fractional integro-differentiation operator.

According to the requirements of the tender documentation, the following will be published:

– at least 3 (three) articles and (or) reviews in peer-reviewed scientific publications on the scientific direction of the project, included in 1 (first), 2 (second) or 3 (third) quartiles in the Web of Science database;

– at least 5 (five) article or review in a peer-reviewed foreign or domestic publication recommended by CCESME MOS RK;

– or at least 1 (one) article or review in a peer-reviewed scientific publication included in 1 (first) quartile in the Web of Science database.

Research group:

  1. Baishemirov Zharasbek, PhD, Associate Professor, Project Supervisor, Chief Researcher

Scopus AU-ID: 55817472800

ORCID: 0000-0002-4812-4104

Web of Science Researcher ID:  AAD-8778-2021

  1. Akhtaeva Nazgul, PhD, Acting Associate Professor, Chief Researcher

Scopus AU-ID: 55755778000

  1. Ryskan Ainur, PhD, senior lecturer, Researcher

Scopus AU-ID: 57209534432

ORCID: 0000-0002-8764-4751

  1. Abdiramanov Zhanars, PhD student, Researcher

Scopus AU-ID: 57219802387

  1. Baimurzayev Zhomart, Master, Researcher
  2. Adil Nauryzbay, PhD student, Researcher