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Research Laboratory «Group Analysis of Mathematical Models in Natural sciences, Engineering and Technology

Invited researcher Nail Khairullovich Ibragimov
Contract number
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As of 30.01.2020

Number of staff members
scientific publications
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General information

Name of the project: Mathematical modeling and group analysis of differential equations

Strategy for Scientific and Technological Development Priority Level: а

Goals and objectives

Research directions: Group analysis of differential equations of fractional and integer order, mathematical and computer modeling of processes and systems, 3D visualization of results of computer modeling

Project objective: Development of the scientific school in the domain of mathematical modeling based on new methods of group analysis and their applications for studies of models in science and technology

The practical value of the study

  • Our researchers have proposed a method for obtaining precise solutions of nonlinear differential equations and systems of those.
  • We have build new conservation laws for mathematical models described by differential equations of fractional and integer order, solved problems of their group classification, developed methods of their precise and approximate integration.
  • Our researchers have developed models of collectors of oil and gas deposits with complex geological structure and permeability, as well as models of filtration of oil and gas in them.
  • The Laboratory has developed schemes of 3D visualization for computer models and software that has been tested on a 3D testing bench.
  • We have created an intellectual database in group analysis with mathematical models from various domains of natural sciences, engineering, and technology.

Implemented results of research:

  • The proposed mathematical model for friction welding using heat during tight pressing of parts can be applied in technologies of manufacturing of blisks of aircraft engines.
  • The developed models for processes of movement of oil and gas in collectors with complex structures allow to predict volumes of hydrocarbon extraction from oil and gas deposits of Russia and are used in scientific and practical work of «RN-UfaNIPINeft» LLC that is a project institute of Rosneft Oil Company.

Education and career development:

  • We have organized internships of students, postgraduates and young scientists at leading foreign universities: the Blekinge Institute of Technology (Sweden), the School of Mathematics of the Suranaree University of Technology (Thailand), Brock University (Canada), the University of Cádiz (Spain), and the Shenyang Aerospace University (China PR).
  • Two doctoral dissertations and 3 candidate dissertations have been defended.
  • We have developed educational courses: «Analytical methods of solving differential equations» (bachelors) and «Mathematical modeling with elements of group analysis» (for masters), and the short-term additional training course «Methods of research of symmetry properties of mathematical models». A masters program in mathematics has been developed, as well as a distance education course in applications of group transformations in mathematical modeling (in Russian and English)

Organizational and structural changes:

  • New infrastructure has been build for conducting scientific research and completing applied work in mathematical modeling that is being successfully enhance after the completion of the project.
  • A unique bench for 3D visualization for research and education purposes has been created and is currently functioning.
  • We are regularly modernizing the university's supercomputer.
  • The Laboratory has purchased professional software for computer modeling.

Other results: We have conducted four international conferences: «Modern Group Analysis» (MOGRAN): MOGRAN-15 (2012, Kemer, Turkey), MOGRAN-16 (2013, Ufa, Russia), MOGRAN-17 (2014, Cádiz, Spain), MOGRAN-18 (2015, Shenyang, China PR).


  • Blekinge Institute of Technology (Sweden): a bilateral agreement for conducting joint scientific research in group analysis of mathematical models, and a trilateral agreement (in collaboration with the Federal University of ABC, Brazil) for partnership in staff training in mathematical modeling and group analysis (we have organized internships of young members of the academic staff of the Laboratory, students, postgraduates and young researchers at the Blekinge Institute of Technology; as a result of research in collaboration with employees of the Institute we have published several articles in journals indexed by the «Web of Science» database).
  • University of Cádiz (Spain): a bilateral agreement for joint research in group analysis of differential and integro-differential equations and training staff in applied mathematics (joint participation of two universities in the «Erasmus Mundus» program that resulted in postgraduate exchange, several articles have been published in journals indexed by the «Web of Science» database).
  • Federal University of ABC (Brazil): a bilateral agreement for collaborative scientific research in group analysis of mathematical models and a trilateral agreement (in collaboration with the Blekinge Institute of Technology, Sweden) for partnership in staff training in mathematical modeling and group analysis (joint events have been conducted, several articles have been published in journals indexed by the «Web of Science» database)

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Baikov V.A., Ibragimov N.H., Zheltova I.S., Yakovlev A.A.
Conservation Laws for Two-Phase Filtration Models. Communications in Nonlinear Science and Numerical Simulation 19(2): 383–389 (2014).
Gazizov R.K., Ibragimov N.H., Rudenko O.V.
Effect of Resonant Absorption in Viscous and Dry Vibrating Contact: Mathematical Models and Theory Connected with Slow Dynamics and Friction Welding. Communications in Nonlinear Science and Numerical Simulation 19(2): 337–344 (2014).
Gazizov R.K., Ibragimov N.H., Lukashchuk S.Yu
Nonlinear Self-Adjointness, Conservation Laws and Exact Solutions of Time-Fractional Kompannets Equations. Communications in Nonlinear Science and Numerical Simulation 23(1-3): 153–163 (2015).
Ibragimov N.H., Gainetdinoiva А.А.
Three-Dimensional Dynamical Systems Admitting Nonlinear Superposition with Three-Dimensional Vessiot-Guldberg-Lie Algebras. Applied Mathematics Letters 52: 126–131 (2016).
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