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Cherniha Roman

# Cherniha Roman

### Education

1976—1981 : Kyiv Taras Shevchenko State University (now: Taras Shevchenko National University of Kyiv), 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;

### Dissertations

1987: Ph.D. dissertation 'Symmetry and exact solutions of some Galilei-invariant nonlinear differential equations'. Institute of Mathematics, NAS of Ukraine, Kyiv. Supervisor: Prof. Wilhelm Fushchych.

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

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

### Research interests

Research interests
Research Summary

My current activity is mostly focused on
• the final stage of preparing the monograph ‘Nonlinear reaction-diffusion-convection equations: conditional symmetry, exact solutions and their applications’ (O.Pliukhin and M. Serov are the co-authors) to be published in 2018 by CRC/Press, Taylor&Francis Group .
• serving as the member of Editorial Board of SYMMETRY http://www.mdpi.com/journal/symmetry/editors
• serving as the co-leader of the Ukrainian-Polish project ‘Mathematical models of hydration-related structural tissue deformations’
• serving as the member of the Science Committee of the National Council for Science and Technology Development of Ukraine

I have a wide range of research interests and am looking for prospective PhD students and /or collaborators within the following topics

• 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, arising in mathematical physics and mathematical biology

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

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

Main research results

• 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 (the results published in papers [3, A1, A2, A4, A5] listed in Publications) .
• 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 [1, 13,16,27].
• A new algorithm for solving group classification (Lie symmetry classification) problems based on the classical Lie-Ovsiannikov 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-Ovsiannikov 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 [5,9—11,14,15,17—19,23, 41, A14].
• 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 [4, 6, 7,8,12,17, 25, A8, A9, A10].
• 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 [5,21,22,34,A13, A16].
• 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 three-component 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). [28,30,32,33,38,39].
• 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. [26,29,31,36, 40, A15].
• Some two- and multi-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 [2,26,29, 31, A3].
• New mathematical models describing fluid transport in peritoneal dialysis are developed. The models are nonlinear BVPs based on nonlinear systems of two-dimensional partial differential equations for fluid and solute transport from the tissue to the peritoneal cavity. 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 [20,37,A11, A12].

### Experience

Research experience

• 1981–1992 : Research Assistant and Research Associate, Institute of Technical Heat Physics, Ukrainian Academy of Sciences, 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 http://www.imath.kiev.ua/people/profile.php?pid=110&tab=2&lang=en

• From September 2013 – June 2015: Marie Curie Research Fellow, School of Mathematical Sci., University of Nottingham, UK
https://www.nottingham.ac.uk/

Pedagogical experience

• Sept. 1987—June 1988: Assistant professor (part-time position), Department of Mathema-tics of Kyiv Polytechnic Institute (now National University ‘Kyiv Polytechnic Institute’)
• Sept. 2004—Sept.2009: Professor (part-time position), Department of Applied Mathematics of University ‘Inter-regional Academy of Personal Management’, Kyiv, Ukraine
• Sept. 2007 – May 2010: Professor (part-time position), Department of Mathematical Physics, Lesya Ukrayinka Volyn National University, Lutsk, Ukraine
• From May 2010— June 2014: Professor (part-time position), Department of Mathematics, National University ‘Kyiv Mohyla Academy’, Kyiv, Ukraine http://ukma.kiev.ua/eng_site/

### Talks on conferences

Participation in major most recent international conferences (2014—2017):

• International Conference on Symmetry Methods, Applications, and Related Fields, Vancouver, Canada, May 13—16, 2014 (plenary talk) http://www.pims.math.ca/files/Abstracts-preliminary.pdf
• BIOMAT 2014 – 14th International Symposium on Mathematical and Computional Biology, Bedlewo, Poland, 2—8 November, 2014 (plenary talk) http://biomat.org/biomat2014/scientificprogramme2014v3.pdf
• 14-th International Conference Geometry, Integrability and Quantization, Varna, Bulgaria, June 6—12, 2014 (plenary talk) http://www.bio21.bas.bg/conference/Varna_14.htm
• 9th European Conference on Mathematical and Theoretical Biology, Gothenburg, Sweden (two session talks) June 14—19, 2014http://conferences.chalmers.se/index.php/ecmtb/ecmtb/paper/view/1319
• International Conference on Free Boundary Problems: Theory and Applications, Cambridge, UK, 23 – 27 June, 2014 (session talk) http://www-old.newton.ac.uk/programmes/FRB/seminars/2014062511151.html
• 10th AIMS International Conference on Dynamical Systems, Differential Equations, and Applications, Madrid, July 7—11, 2014 (session talk) http://www.aimsciences.org/conferences/2014/session_schedule/ps08ss115.pdf
• BIOMAT 2014 – 14th International Symposium on Mathematical and Computional Biology, Bedlewo, Poland, 2—8 November, 2014 (plenary talk)http://biomat.org/biomat2014/scientificprogramme2014v3.pdf
• The Joint British Mathematical Colloquium & British Applied Mathematics Colloquium 2015, Cambridge, 30th March – 2nd April, 2015 (section talk). http://www.bmc-bamc2015.maths.cam.ac.uk/proceedings/abstract.php?id=46
• The 9th International Conference on Differential Equations and Dynamical Systems, Dallas, Texas, USA, May 14-16, 2015 (plenary talk)http://www.watsci.org/deds2015/
• The 7th European Congress of Mathematics, Berlin, July 18-22, 2016. http://www.7ecm.de/program/contributed_talks.html (two session talks).
•SIAM Annual Meeting, Pittsburgh, USA, July, 2017 (section talk)
http://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=62608
• Symmetry 2017- The First International Conference on Symmetry, Barcelona, Spain, October 16-18, 2017 (plenary talk) http://sciforum.net/conference/symmetry2017/symmetry2017-S4

Main conferences ( 2000--2013):

•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.
•Workshop devoted to the Professor Fushchych memory at Institute of Mathematics, Kyiv, Ukraine (plenary talk), December 21-22, 2013

I was the organizer of minisymposias (special sessions) at the following conferences
• 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.
• SIAM Annual Meeting, Pittsburgh, USA, July, 2017
http://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=62608

### Miscellaneous

Awards

• March 2008: Visiting professor for a month, Departement de Physique de la Matiere et des Materiaux, Institut Jean Lamour, Universite Nancy, Nancy, France
• May- June 2009: Visiting professor for a 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)
• May 2017: was elected as a member of the Scientific Committee of the National Council on the Science and Technology Development of Ukraine

2001—2004: The Royal Society (London) 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—2015: Marie Curie Individual International Incoming Fellowship Grant ‘Reductions and exact solutions of boundary value problems with moving boundaries by means of symmetry based methods’ (Project number 328563). The project funded by EU within FP7-PEOPLE-2012-IIF https://www.facebook.com/BVPsymmetry/info?tab=overview

2016—2017: Return Phase of the project ‘Reductions and exact solutions of boundary value problems with moving boundaries by means of symmetry based methods’ (Project number 912563) funded by EU within FP7-PEOPLE-2012-IIF

2018—2020: The project ‘Mathematical models of hydration-related structural tissue deformations’ (together with Prof. J.Waniewski). The project funded jointly by NAS of Ukraine and Polish Academy of Sciences

Other professional activities (since 2000 only)

International Scientific Visits (with duration one week and more)

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, Oct.2012 and May 2014.
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.
Visiting professor IBIB of Polish Academy of Sciences, Warszawa (Poland). Nov.—Dec. 2015.
Visiting professot . University of Nottingham (England). March—April, 2017

I was the organizer of minisymposias (special sessions) at the following conferences

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.

SIAM Annual Meeting, Pittsburgh, USA, July, 2017
http://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=62608

Proffesional Service

• The Editorial Board member of the journal SYMMETRY http://www.mdpi.com/journal/symmetry/editors

• Served as Guest Editor-in-Chief for the following special issues of the SYMMETRY journal:
Lie Theory and Its Application, 2015 http://www.mdpi.com/journal/symmetry/special_issues/lie_theory
Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models, 2016
http://www.mdpi.com/journal/symmetry/special_issues/Lie_Conditional_Symmetries
Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models, II. 2017
http://www.mdpi.com/journal/symmetry/special_issues/Lie_Cond_symmetries

• Acted as the referee for several international scientific journals including: J. of Mathematical Analysis and Applications, Reports on Mathematical Physics, J. of Engineering Mathematics, Applied Mathematics Letters, Math.& Comp. Modelling, Phys. Scripta, Com. Nonlin. Sci.& Num.Sim., J. Phys. A:Math. Teor., Applied Mathematics & Computation, Intl. J. of Heat & Mass Transfer, IJDSDE, Appl. Math. & Comp., Proc. Roy. Soc.A.

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 2014)

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

•Society for Industrial and Applied Mathematics (SIAM) (since 2017) https://www.siam.org/membership/

Teaching and supervising

Supervisor of the following Ph.D. Thesis:
• Oleksii Pliukhin 'Conditional symmetries and exact solutions of reaction-diffusion systems with po wer coefficients of diffusion’ (successfully defended in May, 2009)
• Liliia Myroniuk ' Symmetries and exact solutions of non-linear systems with cross- diffusion' (successfully defended in June, 2011)
• Sergii Kovalenko ‘Exact solutions of some nonlinear boundary value problems with moving boundaries’ (successfully defended in October, 2012)
• Vasyl’ Davydovych ‘Reaction–diffusion systems: conditional symmetries, exact solutions and their properties’ (successfully defended in February, 2014)

Supervisor of the following Master Thesis:
• Iryna Patiyuk 'Lie symmetries and exact solutions of an equation that occurs in modelling turbulent flows.' (defended with Honours, 2008)
• Iryna Polishchuk ' Constructing exact solutions and investigation of their properties for a diffusive Lotka-Volterra type system' (defended with Honours, 2008)
• Vasyl’ Davydovych 'Constructing exact solutions and investigation of their properties for a nonlinear model arising in mathematical biology’ (defended with Honours, 2009)
• Maksym Didovych ' Exact solutions of the simplified Keller-Segel model' (defended with Honours, 2013)
• Nikita Kruk ‘Investigation of a nonlinear problem for modelling processes of melting and evaporation(defended with Honours, 2014)
• Kateryna Gozak ‘New non-uniform steady-state solutions of a mathematical model for fluid and solute transport in peritoneal dialysis `(defended with Honours, 2015)

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' (from 2005 till 2013);
• Mathematical Biology: for graduate and undergraduate students with specialization 'mathematics' and 'applied mathematics' (from 2006 till 2013);
• Nonlinear Differential Equations: for graduate students with specialization 'applied mathematics' (from 2012 till 2014)

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

Languages: Ukrainian (native speaker), English (very good), Russian (very good),
Polish and German (basic communicative skills, reading, translation)

E-mail: r.m.cherniha@gmail.com (not cherniha@imath.kiev.ua !)

Last time updated: 29th Dec 2017