Contact
Biography
Educational Data and Scientific Degrees/Titles:
• 1976-1981: Kyiv Taras Shevchenko State University (now: Taras Shevchenko National University of Kyiv), Faculty of Mechanics and Mathematics, M.Sc. with Honours.
•1987: Ph.D. dissertation. Institute of Mathematics, NAS of Ukraine, Kyiv. Supervisor: Prof. Wilhelm Fushchych.
• July 2003: Dr.Sci. dissertation (habilitation), 'Nonlinear evolution equations: Galilei invariance, exact solutions and their applications'. Institute of Mathematics, NAS of Ukraine, Kyiv
• May 2012: Professor in Mathematics (the state title given by the Government of Ukraine for considerable achievements in both scientific and pedagogical activities)
Research Experience:
• 1981-1992: Research Assistant and Research Associate, Institute of Technical Heat Physics, Academy of Sciences of Ukraine, Kyiv
• 1992-2004: Senior Scientist, Department of Applied Research, Institute of Mathematics, NAS of Ukraine
• 2004 - date: Leading Scientist (an equivalent to the professor position at universities), Department of Mathematical Physics, Institute of Mathematics, NAS of Ukraine, Kyiv
• 2003, 2008 and 2009: Researcher (temporary CNRS position), Laboratoire de Physique des Materiaux, Universite Henri Poincare Nancy I, Nancy, France
• 2013-2015: Marie Curie Research Fellow, School of Mathematical Sciences, University of Nottingham
Pedagogical Experience:
• Sept. 2004 - Sept. 2009: Professor (part-time position), Department of Applied Mathematics of University 'Inter-regional Academy of Personal Management', Kyiv
• Sept. 2007 - May 2010: Professor (part-time position), Department of Mathematical Physics, Lesya Ukrayinka Volyn National University, Lutsk, Ukraine
• May 2010 - June 2014: Professor (part-time position), Department of Mathematics, National University 'Kyiv Mohyla Academy', Kyiv
Expertise Summary
Main fields of research
• Non-linear partial differential equations (PDEs): Lie and conditional symmetries, exact solutions and their properties
• Development of new methods for analytical solving non-linear PDEs
• Application of modern methods for analytical solving nonlinear boundary value problems (including those with moving boundaries) , arising in mathematical physics and mathematical biology.
• Development of mathematical models describing real-world processes arising in physics, biology and medicine.
Circa 120 scientific papers and 3 books are published up to date the 1st Jan, 2022 ( conference thesis and preprints are not taken into account). According to the WEB of Science (Core collection) data base, 68 papers among them were indexed, which were cited 807 times and the Hirsch index is h=18 (up to date Jan 1, 2022). According to the Scopus data base 78 papers were indexed, which were cited 980 times and the Hirsch index is h=20 (up to date Jan 1, 2022).
The list of my books:
Roman Cherniha and Vasyl' Davydovych. Nonlinear reaction-diffusion systems -- conditional symmetry, exact solutions and their applications in biology. -- Lecture Notes in Mathematics. Vol. 2196 .Springer , 2017. https://www.springer.com/gp/book/9783319654652
R. Cherniha, M. Serov, O. Pliukhin. Nonlinear reaction-diffusion-convection equations: Lie and conditional symmetry, exact solutions and their applications. CRC Press (USA), 2018. https://www.taylorfrancis.com/books/9781498776196
`Lie and Non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models.' Edited by Roman Cherniha. MDPI, Basel, 2017. https://www.mdpi.com/books/pdfview/book/369
Research Summary
My current research is mostly focused on the aims and activities described in the application for the British Academy Researchers at Risk Fellowship. In particular:
• conducting research in order to obtain new theoretical results for further development of the conditional-symmetry concept for partial differential equations (PDEs)
• application of existing state-of-the-art symmetry-based methods and new theoretical results in the investigation of real-world models based on systems of nonlinear PDEs. In particular, new Lie and non-Lie symmetries, exact solutions and their physical (biomedical) interpretations will be derived;
• presentation a series of seminars on the research area for researchers and PhD students with specializations in Applied Mathematics and Mathematical Physics
My current research is also focused on
• developing (partly) integrable mathematical models describing the COVID-19 pandemic, exact solving of the models derived and comparison of the results with available data from public sources
• serving as a member of Editorial Board of the international journals SYMMETRY, AXIOMS and a reviewer of several others (Commun. Nonl. Sci. Num. Sim.; Chaos, Solitons & Fractals; Mathematics etc.)
Past Research
Main research results obtained since 1980s till 2020.
• All possible two-component systems of quasilinear parabolic equations, which are invariant under the Galilei algebra and its standard extensions (including the Schroedinger algebra), are constructed; new exact solutions of several physically and/or biologically motivated Galilei-invariant systems are found
• New classes of strongly non-linear second-order PDEs and systems, which are Lie and/or conditionally invariant under conformal Galilei algebra, exotic conformal Galilei algebra and some infinity-dimensional extensions of Galilei algebra are constructed. Examples of new PDEs and systems with physical interpretation are proposeded
. • A new algorithm for solving group classification (Lie symmetry classification) problems based on the classical Lie method and form-preserving transformations, is proposed. Using this algorithm, a complete description of Lie symmetries of the general reaction-diffusion-convection equation (involving arbitrary functions in diffusion, convection and reaction terms) is derived and it is shown that the algorithm is more efficient for solving Lie symmetry classification problems than the classical Lie method. Lie symmetry classification problems are solved also for two-component systems of multidimensional reaction-diffusion (RD) equations (involving arbitrary functions in the diffusion and reaction terms), for the generalized thin film equation (involving three arbitrary functions) and for a class of RD equations with gradient-dependent diffusivity.
• New algorithm, called the method of additional generating conditions, for construction exact solutions of nonlinear PDEs with poor (trivial) Lie symmetry is worked out. Using this algorithm, new exact solutions of several physically, biologically and chemically motivated non-linear PDEs and systems are constructed and their interpretation are demonstrated .
• A complete description of Q-conditional (non-classical) symmetries for the most common subcases of the general reaction-diffusion-convection equation is obtained. The results are successfully applied for constructing new exact solutions for nonlinear PDEs arising in modeling of some real world processes .
• New definitions of Q-conditional symmetry for systems of PDEs are presented,which generalize the standard notation of non-classical symmetry. It is shown that different types of Q-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. Two- and threecomponent Lotka-Volterra systems of reaction-diffusion equations were examined in order to demonstrate the applicability of the definitions for finding new symmetries and constructing exact solutions with biological interpretation. The results are extended on the general two-component RD systems (involving arbitrary functions in the diffusion and reaction terms).
• New definitions of the Lie and conditional invariance for boundary-value problems (BVP) with a wide range of boundary conditions (including those on infinity and moving surfaces) are formulated and an algorithm of the Lie symmetry classification for the given class of BVPs is worked out. The results are generalized in order to introduce the notion of conditional symmetry of BVP. Successful applications of these definitions for the Lie and conditional symmetry classification of some classes of nonlinear BVPs (including multi-dimensional those) are realized. [26.
• Two- and three-dimensional BVPs with moving boundaries (Stefan problems), describing processes of melting and evaporation of materials, are examined by symmetry based methods in order to find their exact solutions. A physical interpretation of the exact solutions obtained are proposed. Some exact solutions are also compared with those obtained by numerical simulations.
• New mathematical models describing fluid transport in peritoneal dialysis and poroelastic materials are developed. The models are developed in the form of nonlinear BVPs based on nonlinear systems of two-dimensional partial differential equations. Exact solutions of the models are constructed under some biologically motivated assumptions and compared with experimental data. The models are also solved using numerical methods .
• New Q-conditional symmetries (nonclsssical symmetries) and exact solutions (including traveling fronts) of the three-component reaction-diffusion systems with quadratic nonlinearities describing some social processes are constructed. The results are used for simulation of such known social phenomena as the competition of different-language speakers and the interaction of hunter-gatherer and farmer populations.
The afore-listed results are reflected in 120 research papers and 3 books (up to date the 1st Jan, 2022; thesis of conferences and preprints are not taken into account). According to the WEB of Science (Core collection) data base, 68 papers among them were indexed, which were cited 807 times and the Hirsch index is h=18 (up to date Jan 1, 2022). According to the Scopus data base 78 papers were indexed, which were cited 980 times and the Hirsch index is h=20 (up to date Jan 1, 2022).
The list of my books:
Roman Cherniha and Vasyl' Davydovych. Nonlinear reaction-diffusion systems -- conditional symmetry, exact solutions and their applications in biology. -- Lecture Notes in Mathematics. Vol. 2196 .Springer , 2017. https://www.springer.com/gp/book/9783319654652
R. Cherniha, M. Serov, O. Pliukhin. Nonlinear reaction-diffusion-convection equations: Lie and conditional symmetry, exact solutions and their applications. CRC Press (USA), 2018. https://www.taylorfrancis.com/books/9781498776196
`Lie and Non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models.' Edited by Roman Cherniha. MDPI, Basel, 2017. https://www.mdpi.com/books/pdfview/book/369
Future Research
TBA