Roman Taranets

• Undergraduate and graduate studies
  Institution: Donetsk State University, Faculty of Mathematics (1994–1999)
  Degree: Master of Sciences in Mathematics (1999)
  Field of Study: Non-linear PDE analysis and Applied Mathematics
• Postgraduate study
  Institution: Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine (1999–2002)
• Ph.D. in Mathematics
  Institution: Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine (2006)
  Name of Theses: Solvability and qualitative properties of solutions of capillary thin-film equation with nonlinear diffusion, convection and absorption (2006)
  Supervisor: Prof. A. Shishkov (Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine)
• Doctor of Physical and Mathematical Sciences
  Institution: Taras Shevchenko National University of Kyiv (2019)
  Name of Theses: Qualitative analysis of higher-order nonlinear parabolic equations and systems (2019)

Monographs and Books

Marina Chugunova, Roman Taranets, Mathematical theory of higher-order degenerate evolution models, PH ”Akademperiodyka”, 230p., 2019 (ISBN: 978-966-360-382-7)

Articles

Chugunova M., Taranets R., Vasylyeva N. Initial-boundary value problems for conservative Kimura-type equations: solvability, asymptotic and conservation law. J. Evol. Equ. 23, Article number: 17 (2023).

Oleksiy V. Kapustyan, Pavlo O. Kasyanov, Roman M. Taranets, Strong solutions and trajectory attractors to the thin-film equation with absorption, J. Math. Anal. Appl., 493 (2), 124562 (2021)

Marina Chugunova, Y. Ruan, Roman Taranets, On qualitative behaviour of solutions to a thin film equation with a source term, Journal of Nonlinear Science, 31, Article number: 9 (2021).

Casey Johnson, Roman M. Taranets, Nataliya Vasylyeva, Marina Chugunova, Existence and Stability Analysis of Solutions for an Ultradian Glucocorticoid Rhythmicity and Acute Stress Model, Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, Understanding Complex Systems, eds. V.A. Sadovnichiy and M. Zgurovsky, Springer, Cham, 165-194 (2021).

J.L. Marzuola, S.R. Swygert, R. Taranets, Nonnegative weak solutions of thin-film equations related to viscous flows in cylindrical geometries, Journal of Evolution Equations, 20 (December), 1227-1249 (2020).

G. Kitavtsev, R.M. Taranets, Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics, Interfaces and Free Boundaries, 22 (2), 157-174 (2020).

M. Chugunova, M.G. Doyle, J.P. Keener, R.M. Taranets, Use of mathematical modeling to study pressure regimes in normal and Fontan blood flow circulations, Mathematics-in-Industry Case Studies, 10 (1), 1-28 (2019).

R.M. Taranets, Finite speed of propagation for the thin film equation in spherical geometry, Ukrainian Mathematical Journal, 71 (6), 956-969 (2019).

R.M. Taranets, Strong solutions of the thin film equation in spherical geometry, Modern Mathematics and Mechanics, Understanding Complex Systems, eds. V.A. Sadovnichiy and M. Zgurovsky, Springer International Publishing AG, part of Springer Nature, Chapter 11, 181-192 (2019).

R.M. Taranets, Thin-film flows on a solid sphere, Journal of Mathematical Sciences, 243 (3), 493-504 (2019).

M. Chugunova, R. Taranets, Thin film flow dynamics on fiber nets, Communications in Mathematical Sciences, 16 (3), 763-775 (2018).

M. Chugunova, R. Taranets, Longtime dynamics of the PDE model for the motion toward light of bacterial colonies, Nonlinearity, 31 (3), 887-908 (2018).

M. Chugunova, R. Taranets, Theoretical aspects of a binary mixture flow, Computers and Mathematics with Applications, 75 (11), 3957-3970 (2018).

Jeffrey Wong, Roman M. Taranets, Existence of weak solutions for particle-laden flow with surface tension, Discrete and Continuous Dynamical Systems: Series A, 38 (10), 4979-4996 (2018).

M. Fontelos, G. Kitavtsev and R. Taranets, Asymptotic decay and non-rupture of viscous sheets, Zeitschrift für angewandte Mathematik und Physik, 69 (3): 79, 21 p. (2018).

Igor B. Krasnyuk, Roman M. Taranets, Marina Chugunova, Dynamic boundary conditions in the interface modeling of binary alloys, AIMS Mathematics, 3 (3), 409-425 (2018).