Ukrainian version Roman CHERNIHA

Postal address: Institute of Mathematics, Ukrainian National Academy of Sciences

Tereshchenkivs`ka Street , 3, 01601 Kyiv (Kiev) , UKRAINE

E-mail address: cherniha@imath.kiev.ua

Fax: +380-44-235-20-10, Phone: +380-44-452-83-39

Internet: www.cherniha.org.ua

CURRICULUM VITAE

Personal Data Born: 21 December, 1958, Lviv region, Ukraine. Citizen of Ukraine. Married to Nataly Cherniha. Two children: Bohdan (1982) and Nazar (1987)

Educational Data

1976-1981 : Kyiv 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, NAS of Ukraine, Kyiv. Thesis Advisor: Wilhelm Fushchych.

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

Professional Experience

Aug.1981 — Dec. 1992 : Engineer, Research Assistant and Research Associate, Institute of Technical Heat Physics, Ukrainian Academy of Sciences, Kyiv, Ukraine

From Dec.1992-- till now: Leading Scientist (Senior Research Fellow), Department of Applied Research, Institute of Mathematics, NAS of Ukraine, Kyiv, Ukraine.

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

From Sept. 2004– till now: Professor (part-time position), Department of Applied Mathematics, Inter-regional Academy of Personal Management, Kyiv, Ukraine.

From Sept.2007 – till now: Professor (part-time position), Faculty of Mathematics and Informatics, Lesya Ukraїnka Volyn National University, Lutsk, Ukraine.

March 2008: Professor (temporary position), Laboratoire de Physique des Materiaux, Universite Henri Poincare Nancy I, Nancy, France.

International Scientific Visits

• Visiting scholar, Ervin Schroedinger Institute of Mathematical Physics, Wien (Austria), October 1994 ;

• Visiting scholar, Mathematisches Institut Oberwolfach, Oberwolfach (Germany), Jan.--Febr.1996;

• Visiting scholar, Worcester Polytechnic Institute, Worcester (USA), Nov.1996;

• Visiting professor, Technische Hochschule Darmstadt (Germany), March 1997;

• Visiting professor, University of Nottingham (England), Oct.--Dec. 1998;

• Visiting professor, Glasgow Caledonian University (Scotland), Dec. 1998;

• Visiting professor, Mathematisches Institut Oberwolfach, Oberwolfach (Germany), Nov.-- Dec. 1999, Oct.--Nov. 2006;

• Visiting scholar, IBIB of Polish Academy of Sciences, Warszawa (Poland). May and Nov. 2001; Apr.2002; March and Oct. 2003; Oct. 2004; July 2005, June 2006, July 2007; June 2008.;

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

• Visiting professor, Universite Henri Poincare Nancy I, Nancy ( France), Nov. 2006.

Participation in major international conferences

• First , Second, 4-th, 5-th, 6-th and 7-th International Conferences "Symmetry in Nonlinear Mathematical Physics" , Kyiv (Ukraine) , July 1995, July 1997, July 2001, June 2003, June 2005 and June 2007, respectively.

• 28-th , 31-st and 33-rd Symposiums on Mathematical Physics, Torun (Poland), Dec.1995, May 1999 and June 2001, respectively.

• Third European Conferences on Mathematics applied to Biology and Medicine, Heidelberg (Germany), October 1996.

• Fifth International Conference on Mathematical Population Dynamics, Zakopane (Poland), June 1998.

• International Congress of Mathematicians, Berlin, August 1998.

• First and Second International Workshops on Similarity Methods, Stuttgart (Germany), November 1998 and November 1999.

• 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 (Ukraine), May 2004.

• Sixth European Conferences on Mathematics applied to Biology and Medicine, Dresden (Germany), July 2005.

• XXV Dynamics Day Europe, Berlin, July 2005.

• Sixth International Congress on Industrial and Applied Mathematics, Zurich, July 2007.

Fields of Research

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

• Non-linear PDEs: symmetry analysis, exact solutions and their properties.

• 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 (Stefan type problems).

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

Pedagogical Activity

• Advisor of the following Ph.D. Thesis:

Oleksii Pliukhin 'Conditional symmetries and exact solutions of reaction-diffusion systems with power coefficients of diffusion.' (to be completed in 2009)

Liliia Myroniuk ' Symmetries and exact solutions of non-linear systems with cross diffusion' (to be completed in 2009)

• Advisor of the following Master .D. Thesis:

Iryna Patiyuk 'Lie symmetries and exact solutions of an equation that occurs in modelling turbulent flows.' (with Honours, 2008)

Iryna Polishchuk ' Constructing exact solutions and investigation of their properties for a diffusive Lotka-Volterra type system' (with Honours, 2008)

• Courses of lectures:

• Mathematical Analysis -- for undergraduate students with specialization 'applied mathematics' (since 2004 );

• Complex Analysis -- for undergraduate students with specialization 'applied mathematics' (since 2005);

• Equations of Mathematical Physics -- for undergraduate students with specialization 'applied mathematics' (since 2005 )

• Mathematical Biology -- for undergraduate and graduate students with specialization 'mathematics' and 'applied mathematics' (since 2006 )

About 100 scientific papers published up to date 01.12.2008.

Papers published in major international journals with impact-index (list of ISI Web of Knowledge )

1. Fushchych W.I and Cherniha R.M The Galilean relativistic principle and nonlinear partial differential equations. J.Phys.A.:Math. and Gen.--1985.-v.18, N 18.--P.3491―3503.

2. Cherniha R. and Cherniha N. Exact solution of a class of nonlinear boundary value problems with moving boundaries. J.Phys.A.:Math. and Gen. 1993.-v.26, N 18.--P. L935-940.

3. Fushchych W.I and Cherniha R.M. Galilei-invariant systems of nonlinear systems of evolution equations. J.Phys.A: Math.Gen. -1995. -vol. 28, P.5569-5579.

4. Cherniha R. A constructive method for obtaining new exact solutions of nonlinear evolution equations. Rept. Math. Phys.-1996.- vol. 38, P.301-312.

5. Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms. //European J. of Appl. Math.--1998. - vol. 9, No 5, P.527-542.

6. Cherniha R. New Non-Lie Ansaetze and Exact Solutions of Nonlinear Reaction-Diffusion-Convection Equations. J. Phys. A: Math.Gen. -- 1998.-vol. 31, No 40, P.8179-8198.

7. Cherniha R. and Fehribach J. New exact solutions for a free boundary system. J.Phys. A: Math. and Gen. ― 1998. -- vol. 31, No 16, P.3815-3829.

8. Cherniha R. New Exact Solutions of Nonlinear Reaction-Diffusion Equations. Rept. Math. Phys.-- -- 1998.―V.41, No 2, P. 333-349.

9. Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen. -- 2000.-- V.33, No 2-- P.267-282.

10.Cherniha R. and King J. R. Addendum. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen.-- 2000.-- V.33, No 43-- P.7839-41.

11.Cherniha R. Lie Symmetries of Nonlinear Two-dimensional Reaction-Diffusion Systems. Rept. Math. Phys.--2000.-v.46.--P. 63-76.

12.Cherniha R. and Dutka V. Exact and Numerical Solutions of the Generalized Fisher Equation. Rept. Math. Phys.--2001.-v.47.--P. 393-411.

13.Cherniha R. M. Nonlinear Galilei-invariant PDEs with infinite-dimensional Lie symmetry. J.Math.Anal.Appl.--2001.-v.253.-- P.126-141.

14.Cherniha R and Serov M. Nonlinear Systems of the Burgers-type Equations: Lie and Q-condi-tional Symmetries, Ansaetze and Solutions. J.Math. Anal. Appl.--2003.-v.282.--P.305-328.

15.Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems. II. J. Phys. A: Math. and Gen.--- 2003.-- vol.36. -- P.~405―425

16.Cherniha R. and Henkel M On nonlinear partial differential equations with an infinite-dimensional conditional symmetry. J.Math.Anal.Appl.--2004.-v.298.-- P.487--500.

17.Cherniha R. and King J. R. Nonlinear Reaction-Diffusion Systems with Variable Diffusivities: Lie Symmetries, Ansaetze and Exact Solution. J.Math.Anal.Appl.--2005.-v.308.-- P.11--35.

18.Cherniha R. and King J. R. Lie Symmetries and Conservation Laws of Nonlinear Multidimensional Reaction-Diffusion Systems with Variable Diffusivities. IMA J. Appl. Math. 2006 -

vol. 71 – P.391-408.

19.Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms, II. European J. of Appl. Math. –2006.-

v.17. ―597-605.

20.Cherniha R., Dutka V., Stachowska-Pietka J. and Waniewski J. Fluid transport in peritoneal dialysis: a mathematical model and numerical solutions. Mathematical Modeling of Biological Systems, Vоl..I. Ed. by A.Deutsch et al., Birkhaeuser, P.291-298, 2007

21.Cherniha R. New Q-conditional symmetries end exact solutions reaction-diffusion-convection eduations arising in mathematical biology. J.Math.Anal.Appl. .--2007.-v.326.-- P.783―799.

22. Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of nonlinear -reaction-diffusion-convection equations. J. Phys. A: Math. and Theor.--- 2007.-- vol.40. -- P.10049―10070.

23.Cherniha R., Serov M. and Rassokha I. Lie Symmetries and Form-preserving Transformations of Reaction-Diffusion-Convection Equations. J.Math.Anal.Appl. .--2008.-v.342.-- P.1363―1379.

24. Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of reaction-diffusion systems with power diffusivities. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 185208 (14pp).

25. Cherniha R. and Myroniuk L. New exact solutions of a nonlinear cross-diffusion system. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 395204 (15pp).

Main publications (in English) published in other scientific journals

1. Fushchych W. and Cherniha R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions I. Ukrainian Math.J. -1989.- vol.41, P. 1161-67 .

2. Fushchych W. and Cherniha R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions II. Ukrainian Math.J. -1989.- vol.41, P.1456-63.

3. Cherniga R.M. and Odnorozhenko I.G. Studies of the processes of melting and evaporation of metals under the action of laser radiation pulses. Promyshlennaya Teplotekhnika-1991- vol. 13- P.51-59 (English translation in Heat Transfer Research, USA)

4. Cherniha R. Galilei-invariant non-linear PDEs and their exact solutions. J. Nonlinear Math. Phys. --1995.- vol. 2, P.374-383.

5. Fushchych W.I., Cherniha R. and Chopyk V. On unique symmetry of two nonlinear generalizations of the Schroedinger equation. J. Nonlinear Math. Phys. -1996.-vol.3, P.296-301.

6. Cherniha R. and Wilhelmsson H. Symmetry and exact solution of heat-mass transfer equations in thermonuclear plasma. Ukrainian Math. J. 1996.- vol. 48-- No 9, P.1434—1449.

7. Cherniha R. New spherycally symmetryc solutions of nonlinear Schroedinger equations. J. Nonlin. Math. Phys.-1997.- Vol.4, No.1-2, P.107--113.

8. Cherniha R. Application of a constructive method for obtaining non-Lie solutions of nonlinear evolution equations. Ukrainian Math. J. - 1997.- vol. 49-- No 6, P.910--924

9. Cherniha R. New Exact Solutions of a Nonlinear Reaction-Diffusion Equation Arising in Mathematical Biology and Their Properties. Ukrainian Math. J. 2001.- vol.53--P.1712--1727.

10. Cherniha R. and Dutka V.A. A diffusive Lotka-Volterra system: Lie symmetries, exact and numerical solutions. Ukrainian Math. J. 2004.- vol.56-- P.1665—1675.

11. Cherniha R. and Waniewski J. Exact solutions of a mathematical model for fluid transport in peritoneal dialysis. Ukrainian Math. J. – 2005.- vol. 57-- P.1112--1119.

12. Waniewski J., Dutka V., Stachowska-Pietka J., Cherniha R. Distributed Modeling of Glucose-Induced Osmotic Flow. Advances in Peritoneal Dialysis―2007―vol.23 (Part 1)―P.2―6.

Refereeing

The referee of several international scientific journals including: Journal of Mathematical Analysis and Applications, Reports on Mathematical Physics, Journal of Engineering Mathematics, Applied Mathematics Letters.

Membership in scientific societies

• Kyiv Mathematical Society (since 1993)

• European Society for Mathematical and Theoretical Biology (since 1996)

• Courses of lectures:Co-founder and head (in 2006-2007) of All-Ukrainian Association for European Values in Science

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

Last updated in January, 2009

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