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Roman Cherniha

Marie Curie Research Fellow, Faculty of Science

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Biography

CURRICULUM VITAE

Educational data

1976-1981 : Kyiv (Kiev) Taras Shevchenko State University, Faculty of Mechanics and Mathematics, majoring in mathematical physics;

1981 : M.Sc. with Honours, Kyiv Taras Shevchenko State University;

1983-1987 : Post-graduate courses, Kyiv Taras Shevchenko State University;

1987 : Ph.D. dissertation. Institute of Mathematics, Academy of Sciences of Ukraine, Kyiv.

Supervisor: Prof. Wilhelm Fushchych.

Research experience

1981-1992 : Research Assistant and Research Associate, Institute of Technical Heat Physics, Academy of Sciences of Ukraine, Kyiv, Ukraine

1992 - 2004: Senior Scientist , Department of Applied Research, Institute of Mathematics, NAS of Ukraine, Kyiv, Ukraine

Oct. - Dec. 2003: Scholar (temporary CNRS position), Laboratoire de Physique des Materiaux, Universite Henri Poincare Nancy I, Nancy, France

From 2004 - till now: Leading Scientist (an equivalent to the professor position at universities in Ukraine), Department of Mathematical Methods in Statistical Mechanics (2004- 2007) and Department of Applied Research ( 2007 - till now), Institute of Mathematics, NAS of Ukraine, Kyiv, Ukraine ( Research and academic achievements (since 2000 year only )

Awards:

July 2003: Dr. Sci. dissertation (habilitation) 'Nonlinear evolution equations: Galilei invariance, exact solutions and their applications'. Institute of Mathematics, NAS of Ukraine, Kyiv;

March 2008: Visiting professor for one month, Departement de Physique de la Matiere et des Materiaux, Institut Jean Lamour, Universite Nancy, Nancy, France.

May- June 2009: Visiting professor for one month, Departement de Physique de la Matiere et des Materiaux, Institut Jean Lamour, Universite Nancy, Nancy, France.

May 2012: Professor in Mathematics (the state title given by the Government of Ukraine for the considerable achievements in both scientific and pedagogical activities)

The project leader/co-leader of the international projects:

2001-2004: The Royal Society International Joint Project 14184 'Symmetries and Solutions of Nonlinear Reaction-Diffusion-Convection Systems ' (together with Prof. JR King);

2003-2005: The project 'Applications of modern mathematical methods for solving nonlinear patterns arising in peritoneal dialysis' (together with Prof. J.Waniewski). The project funded jointly by NAS of Ukraine and Polish Academy of Sciences.

2010: The project 'Mathematical models of fluid and solute transport in normal and pathological tissue' funded by the Mianowski Fund (Warsaw, Poland);

2011-2014: The project 'Mathematical modeling of transport processes in tissue during peritoneal dialysis' (together with Prof. J.Waniewski). The project funded jointly by NAS of Ukraine and Polish Academy of Sciences.

2013-2016: Marie Curie Individual International Incoming Fellowship Grand (Project number 328563). The project funded by EU within FP7-PEOPLE-2012-IIF.

The project co-leader of several national projects funded by NAS of Ukraine. The current project is 'Symmetry, Super-symmetry and Integrability of Differential Equations' (2011-2015). The state registration number 0110U008615.

Other professional activities (since 2000 only)

International Scientific Visits

Visiting scholar, IBIB of Polish Academy of Sciences, Warszawa (Poland). May and Nov. 2001; Apr.2002; March and Oct. 2003; Oct. 2004.

Visiting scholar, University of Nottingham (England). May-June, 2002; March-May, 2003; March- April, 2004.

Visiting professor, IBIB of Polish Academy of Sciences, Warszawa (Poland). July 2005, June 2006, July 2007, June 2008; Oct. 2009, May-June, 2010 and Oct.2012.

Visiting professor according to the programm `Research in Pairs' , Mathematisches Forschung Institut Oberwolfach, Oberwolfach (Germany). Oct.-Nov., 2006.

Visiting professor. University of Warsaw, Warszawa (Poland). October, 2011.

Visiting professor. Universite P&M Curie, Paris. November, 2011.

Participation in major international conferences

4th, 5th, 6th, 7 and 8th International Conferences "Symmetry in Nonlinear Mathematical Physics" , Kyiv (Kiev) July 2001, June 2003, June 2005, June 2007 and June 2009, respectively.

33rd Symposiums on Mathematical Physics, Torun (Poland), June 2001.

XXIV International Colloquium on Group Theoretical Methods in Physics, Paris, July 2002.

International Conference on Theoretical Physics, UNESCO, Paris, July 2002.

International Conference "Recent Trends in Kinetic Theory and Its Applications", Kyiv, May, 2004.

6th European Conferences on Mathematics Applied to Biology and Medicine, Dresden (Germany), July 2005.

XXV Dynamics Day Europe, Berlin, July 2005.

6th International Congress on Industrial and Applied Mathematics, Zurich, July, 2007.

5th Baltic-Nordic AGMP Workshop: Algebra, Geometry, and Mathematical Physics. Bedlewo (Poland), October, 2009.

XIX International Colloquium Integrable Systems and Quantum Symmetries, Praha (Prague), 17-19 June, 2010.

8th European Conferences on Mathematics Applied to Biology and Medicine, Krakow (Poland), July, 2011.

7th Baltic-Nordic AGMP Workshop: Algebra, Geometry, and Mathematical Physics. Mulhouse (France), October, 2011.

8th Baltic-Nordic AGMP Workshop: Algebra, Geometry, and Mathematical Physics. Brno (Czech Rep.), October, 2012.

More than 100 scientific papers published up to date 31.12.2013.

36 papers are listed in ISI Web of Knowledge data base and 43 papers are listed in Scopus data base.

Refereeing

Acted as the referee for several international scientific journals including: Journal of Mathematical Analysis and Applications, Reports on Mathematical Physics, Journal of Engineering Mathematics, Applied Mathematics Letters, Math.& Comp. Modelling, Phys. Scripta, Com. Nonlin. Sci.& Num.Sim. and J. Phys. A:Math. Teor.

Membership in scientific societies

Kyiv Mathematical Society http://www.mathsociety.kiev.ua/ (since 1993 till now)

European Society for Mathematical and Theoretical Biology: http://www.esmtb.org/ (since 1996 till now)

Co-founder and head (in 2006-2007) of All-Ukrainian Association for European Values in Science https://sites.google.com/site/ukrsci/

Languages: Ukrainian (native speaker), English (good), Russian (fluent),

Polish and German (basic communicative skills, reading, translation)

Expertise Summary

Fields of research

• Non-linear PDEs: Lie and conditional symmetries, exact solutions and their properties.

• Development of new methods for analytical solving non-linear partial differential equations (PDEs).

• Application of modern methods for analytical solving nonlinear boundary value problems,

arising in mathematical physics and mathematical biology.

•Analytical and numerical solving boundary value problems with moving boundaries (including Stefan problems)

• Development of mathematical models describing the specific processes arising in physics, biology and medicine.

Main research results

  • All two-component systems of quasilinear parabolic equations invariant under the Galilei algebra and its standard extensions (including the Schroedinger algebra) are constructed and new exact solutions of several physically (biologically) motivated Galilei-invariant systems are found (the results published in papers .
  • New classes of strongly non-linear second-order PDEs and systems (conditionally) invariant under conformal Galilei algebra, exotic conformal Galilei algebra and some infinity-dimensional extensions of Galilei algebra are constructed .
  • A modification of the well-known Ovsiannikov method for solving group classification problems based on using additional equivalence transformations, is proposed. Using this modified method, a complete description of Lie symmetries of the general reaction-diffusion-convection equation (involving arbitrary functions in diffusion, convection and reaction terms) is obtained. The same problem is solved also for two-component systems of multidimensional reaction-diffusion equations (involving arbitrary functions in the diffusion and reaction terms) and for the generalized thin film equation (involving three arbitrary functions).
  • New algorithm, called the method of additional generating conditions, for construction exact solutions of nonlinear PDEs with trivial Lie symmetry is worked out. Using this algorithm, new exact solutions of several physically (biologically) motivated non-linear PDEs and systems were found.
  • A complete description of Q-conditional (i.e. 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-component systems of reaction-diffusion equations (including the classical Lotka-Volterra system) were examined to demonstrate the applicability of the definitions for finding new symmetries and constructing exact solutions with physical and biological interpretation.
  • New definitions of invariance of BVP with a wide range of boundary conditions (including those on non-regular manifolds and moving surfaces) is formulated and an algorithm of the group classification for the given class of BVPs is worked out .
  • New mathematical models to describe fluid transport in peritoneal dialysis is developed, exact and numerical solutions of the models are constructed under some biologically motivated assumptions.

More than 100 scientific papers published up to date 31.12.2013.

36 papers are listed in ISI Web of Knowledge data base and 43 papers are listed in Scopus data base.

Teaching Summary

Courses of lectures:

  • Mathematical Analysis: for undergraduate students with specialization 'applied mathematics' ( 2004 -2009);
  • Complex Analysis: for undergraduate students with specialization 'applied mathematics' ( 2005-2008; 2012);
  • Equations of Mathematical Physics: for undergraduate students with specialization 'applied mathematics' ( 2005 -- 2012)
  • Mathematical Biology: for graduate and undergraduate students with specialization 'mathematics' and 'applied mathematics' ( 2006 --2013)
  • Nonlinear Differential Equations: for graduate students with specialization 'applied mathematics' ( 2012-2013)

The textbook: Cherniha R.M. Equations of Mathematical Physics. - Kyiv: Publishing house 'Kyiv-Mohyla Academy', 2012 (In Ukrainian, Summary in English, ISBN 978-966-2410-14-3)

Research Summary

• Non-linear PDEs: Lie and conditional symmetries, exact solutions and their properties.

• Development of new methods for analytical solving non-linear partial differential equations (PDEs).

• Application of modern methods for analytical solving nonlinear boundary value problems,

arising in mathematical physics and mathematical biology.

•Analytical and numerical solving boundary value problems with moving boundaries (including Stefan problems)

Recent Publications

School of Mathematical Sciences

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