Research Laboratory "Group Analysis of Mathematical Models of Science and Technologies"
This laboratory was established as part of a scientific research project supported with a monetary grant awarded by the Government of the Russian Federation under a grant competition designed to provide governmental support to scientific research projects implemented under the supervision of the world's leading scientists at Russian institutions of higher learning (Resolution of the RF Government No.220 of April 9, 2010).
Grant Agreement No.: 11.G34.31.0042
Name of the institution of higher learning:
Federal state budget educational institution of higher professional learning "Ufa State Aviation Technical University"
Fields of scientific research:
Mathematics, mathematical modeling and group analysis of differential equations
1. To design new solution methods for group classification problems of different classes of mathematical models based on differential, integro-differential, and stochastic equations.
2. To design new group analysis methods (solution development methods, preservation laws, solvability criteria) required to study mathematical models with known symmetries.
Key project objectives:
To research broad classes of mathematical models describing gas-hydrodynamic, wave, and diffusion processes in various natural, technical and technological systems using known group analysis methods, as well as new methods designed in the course of the project.
Anticipated scientific outcomes:
1. The project will help create a library of subprograms in computer algebra packages implementing modern group analysis methods.
2. The project will help create an electronic group analysis database accessible via the Internet.
Leading scientist's full name: Nail Khairullovich Ibragimov
Academic degrees and titles:
Doctor of physical and mathematical sciences, professor
Employer and job title:
- Director of the ALGA international research center (Sweden),
- Honorary professor at the Blekinge Institute of Technology (Karlskrona, Sweden);
- Scientific Director of the research laboratory "Group Analysis of Mathematical Models of Science and Technologies" at the Ufa State Aviation Technical University (Russia).
Fields of scientific research
1. Pure mathematics: nonlinear differential equations, groups and Lie algebras, Riemann geometries, symmetries in mathematical modeling, approximate transformation groups, Lie-Bäcklund transformation groups, equation family invariants.
2. Applied mathematics: preservation laws and invariant group solutions in hydrodynamics, mathematical models of financial mathematics, ground water movement in irrigation systems.
3. Mathematical physics: preservation laws in continuum mechanics, de Sitter world, waves in distorted space, conforming symmetry and Huygens principle, nonlinear diffusion.
- Fulbright fellow, USA, October 1976 – March 1977
- USSR State Prize in science and technology, 1987
- "A" ranking by the SAR Foundation for the Development of Scientific Research, 1994-2000
- "Science of the Year" prize from the Blekinge Science Society, Sweden, 2004
- Lagrange Prize for outstanding contribution to nonlinear sciences, Portugal, 2008