Research interests

nonlinear degenerate high-order parabolic equations;

thin-film type equations with nonlinear lowest terms;

nonlinear Maxwell’s equations.

Diplomas

1999 - Specialist diploma in "Mathematics", Donetsk National University;

2006 - Ph.D. in "Mathematics", Institute of Applied Mathematics & Mechanics NAS Ukraine, Donetsk.

 

Grants and awards

2010-2013   European Community’s Seventh Framework Programme (FP7/2007-2013), grant agreement No PIIF-GA-2009-254521 - [TFE]

2006-2008    Scholarship of Ukrainian National Academy of Sciences for young scientists;

2007    Ya.B.Lopatinsky Prize of the Institute of Applied Mathematics and Mechanics of NASU for a series of paper to the thin film equations;

2003–2004    Research grant of Ukrainian National Academy of Sciences: "The investigation of free boundary problems for quasilinear parabolic equation and the study of asymptotic behaviour of eigenvalues for boundary problem in domains with complex structure";

2001&2003  The Premium of the Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences to young scientists (awarded for high scientific achievements).

Career

1994-1999 - student of mathematical department  of the Donetsk National University;

1999-2002 - Ph.D. student in Institute of Applied Mathematics & Mechanics NAS Ukraine;

2002-2003 - engineer in Department of Partial Differential Equations, Institute of Applied Mathematics & Mechanics NAS Ukraine;

2003-2010 - junior scientific researcher, Institute of Applied Mathematics & Mechanics NAS Ukraine;

2010- present time - researcher, Institute of Applied Mathematics & Mechanics NAS Ukraine. 

Activities:

Participation at conferences and schools:

2011   the British Applied Mathematics Colloquium at the University of Birmingham, Birmingham, UK

2008   the LMS Summer School "On Nonlinear Parabolic Equations and Applications", the University of Swansea, Swansea,UK

2007   the International conference of nonlinear partial differential equations dedicated to the memory of I.V. Skrypnik, Yalta, Ukraine

2007    the International Conference dedicated to I.G. Petrovskii, Moscow, Russia

2005   The International conference of nonlinear partial differential equations, Alushta, Ukraine

2004   the International Conference dedicated to I.G. Petrovskii, Moscow, Russia

2003   the International conference of nonlinear partial differential equations, Alushta, Ukraine

2001   the International conference of nonlinear partial differential equations, Kiev, Ukraine

 

Short visits:

07/2009      the University of Toronto, Toronto, Canada

04/2008      the Mathematical Institute of the Academy of Sciences of the Czech Republic, Prague,   Czech Republic

02/2008     the University of Swansea, Swansea, UK

 

 

Publications

1. Chugunova M., Pugh M., Taranets R. Nonnegative solutions for a long-wave unstable thin film equation with convection, SIAM Journal on Mathematical Analysis, V. 42 (4) , 1826-1853 (2010) .
    
    
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2. Chugunova M., Taranets R., New dissipated energy for nonnegative weak solution of unstable thin-film equations, Communications on Pure and Applied Analysis, V. 10 (2), 613-624 (2011)
    
    
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3. I. Krasnyuk, R. Taranets, The spatial-temporal lamellar structures in the confined ideal polymer blends// Journal of Statistical Physics, V. 145 (6), p. 1485-1498 (2011).
    
4. I.B. Krasnyuk, R.M. Taranets, Effect of pressure and pinning of a vortex lattice on the magnetic flux penetration in high-temperature type-II superconductors // High Pressure Physics and Technics, V. 21, no. 4, p. 29-44 (2011) (in Russian)
    
    
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5. I.B. Krasnyuk, R.M. Taranets, V.M. Yurchenko, Self-similar magnetic structures during the vortex-glass to vortex-liquid transition of type II superconductors // Low Temperature Physics, V. 37 (4), p. 287-292 (2011)
    
    
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6. I.V. Boylo, R.M. Taranets, Elastically deformed vortex lattice in high-temperature type-II superconductors, High Pressure Physics and Technics, V. 21, no. 3, p. 53-62 (2011) (in Russian)
    
    
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7. Krasnyuk I., Stephanovich L., Taranets R., Yurchenko V. Cascade process of ordered nano-structures formation in melt crystallization, Materials Science (publishing house “Nauka & Technology”), no. 7 (2009), 8-15.
    
8. Krasnyuk I., Taranets R. Magnetic flux penetration into high-temperature superconductors in the vortex liquid state under the blow-up conditions, Technical Physics., V. 53, 1041-1050 (2008).
    
    
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9. Krasnyuk I., Taranets R. Self-similar distribution in ''giant'' magnetic flux creep, Technical Physics., V. 52, 1247-1251 (2007)
    
    
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10. Krasnyuk I., Taranets R. The spatiotemporal oscillations of order parameter for isothermal model of the surface-directed spinodal decomposition in bounded binary mixtures, Research Letters in Physics. 2009 (2009), Article ID 250203, 4 pages.
     
     
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11. Namlyeyeva Yu.V., Taranets R.M., Yurchenko V.M. Finite speed of the electromagnetic-field propagations in nonlinear isotropic dispersive media, High Pressure Physics and Technics, V. 19, no. 4, p. 44-56 (2009)
     
     
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12. Shishkov A., Taranets R. A singular Cauchy problem for the equation of the flow of thin viscous films with nonlinear convection // Ukrainian Math. J.- 2006.- Vol.58.- No 2.- p. 280-303
     
     
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13. Shishkov A., Taranets R. On the Thin-Film Equation with Nonlinear Convection in Multidimensional Domains // Ukrainian Math. Bulletin.- 2004. – Vol.1.- No 3. – p. 407-450.
     
     
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14. Taranets R. Solvability and global behavior of solutions of the equation of thin films with nonlinear dissipation and absorption // Proc. of IAMM of NASU. –2002. – Vol.7.- p. 192-209. (in russian)
     
15. Taranets R. Propagation of perturbations in equations of thin capillary films with nonlinear absorption // Proc. of IAMM of NASU. – 2003.- Vol.8. – p. 181-194.
     
16. Taranets R. Propagation of perturbations in thin capillary film equations with nonlinear diffusion and convection //Siberian Math. J.-2006.- Vol.47.- No 4.- p. 914-931.
     
     
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17. Taranets R. Solvability and qualitative properties of solutions of capillary thin-film equation with nonlinear diffusion, convection and absorption // PhD thesis, Donetsk, 2005, 166p. (in Russian)
     
     
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18. Taranets R., Shishkov A. Effect of time delay of support propagation in equations of thin films, Ukrainian Math. J., V. 55, 1131-1152 (2003).
     
     
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19. Yu.V. Namlyeyeva, R.M. Taranets, Backward motion and waiting time phenomena for degenerate parabolic equations with nonlinear gradient absorption // Manuscripta Mathematica, V. 136, no. 3-4, p. 475-500 (2011)
     
     
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20. I.B. Krasnyuk, R.M. Taranets, V.M. Yurchenko. Pulse structures of lamellar type in bounded polymer systems, Matematicheskoe Modelirovanie, V.22 (12), p.65-81 (2010) (in Russian)
     
     
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