System Mathematics

Principal Investigator – acad. NAS of Ukraine, Dr. Hab., Prof. Michael Z Zgurovsky,

 

Head – Dr. Hab. Pavlo O Kasyanov

 

Lately due to the intensification of investigation processes in economics, ecology, geophysics, synergy and geoinformatics there appeared the necessity in more detailed studying of nonlinear effects rise, new classes of mathematical models with nonlinear, nonsmooth, discontinuos and multivalued dependence between determinative parameters of problem, control of nonlinear processes and fields problems, long-range problem forecast of state functions of solutions for such problems. The staff of Nonlinear Analysis Laboratory of differential-operator systems of Institute for Applied System Analysis NAS of Ukraine carries out the fundamental research of such problems in the following directions:

1)      nonlinear analysis and control of classes of nonlinear geophysics processes and fields;

2)      properties of solutions the differential-operator inclusions and multivariation inequalities for Earth data analysis problems;

3)      theory of global and trajectory attractors for infinite-dimensional dynamical systems.

Some Recent Scientific Publications:

Monographs:

  • Zgurovsky MZ, Melnyk VS, Kasyanov PO (2010) Evolution Inclusions and Variation Inequalities for Earth Data Processing I. Heidelberg, Springer. doi:10.1007/978-3-642-13837-9
  • Zgurovsky MZ, Melnyk VS, Kasyanov PO (2010) Evolution Inclusions and Variation Inequalities for Earth Data Processing II. Heidelberg, Springer. doi:10.1007/978-3-642-13878-2
  • Zgurovsky, M.Z.; Kasyanov, P.O.; Kapustyan, O.V.; Valero, J.; Zadoianchuk, N.V. Evolution inclusions and variation Inequalities for Earth data processing III. Long-Time Behavior of Evolution Inclusions Solutions in Earth Data Analysis (English) Series: Advances in Mechanics and Mathematics, Vol. 27. Berlin: Springer, 2012, XLI, 330 p. ISBN 978-3-642-28511-0

 

Articles:

 

  • M.Z. Zgurovsky, P.O. Kasyanov, J. Valero Non-coercive evolution inclusions for Sk type operators // International Journal of Bifurcation and Chaos. –  Vol. 20, No. 9 (2010) P. 2823–2834
  • P.O. Kasyanov, V.S. Mel'nik, S. Toscano Solutions of Cauchy and periodic problems for evolution inclusions with multivalued pseudo-monotone maps// Journal of Differential Equations. - Volume 249, Issue 6, 15 September 2010, Pages 1258-1287.
  • O.V. Kapustyan, P.O. Kasyanov, J. Valero Pullback attractors of a class of extremal solutions of the 3D Navier-Stokes equations // Journal of Mathematical Analysis and Applications. – Volume 373, Issue 2, 15 January 2011, Pages 535 – 547.
  • Pavlo Kasyanov, Valeriy Mel'nik, Anna Maria Piccirillo On some approximations and main topological descriptions for special classes of Banach spaces with integrable derivatives// Methods of Functional Analysis and Topology – 2008. – Vol. 14, № 3. – P. 255-270.
  • Zadoyanchuk N.V., Kasyanov P.O.  Faedo–galerkin method for second-order evolution inclusions with Wλ-pseudo-monotone mappings // Ukrainian mathematical journal. – 2009. – v. 61, №2. – P. 236-258.
  • P.O. Kasyanov Multivalued dynamics of solutions of autonomous operator differential equations with pseudomonotone nonlinearity // Mathematical Notes, Volume 92, Numbers 1-2 (2012), 205-218, DOI: 10.1134/S0001434612070231
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Nina V. Zadoianchuk Berge’s theorem for noncompact image sets // Journal of Mathematical Analysis and Applications. – 2013. – Volume 397, Issue 1. – P.255-259. DOI: 10.1016/j.jmaa.2012.07.051
  • Pavlo O. Kasyanov, Luisa Toscano, Nina V. Zadoianchuk A criterion for the existence of strong solutions for the 3D Navier–Stokes equations // Applied Mathematics Letters. – 2013. – Volume 26, Issue 1. – P.-15-17.  DOI: 10.1016/j.aml.2012.08.007
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Nina V. Zadoianchuk Average Cost Markov Decision Processes with Weakly Continuous Transition Probabilities // Mathematics of Operations Research. – 2012, DOI:10.1287/moor.1120.0555
  • Pavlo O. Kasyanov, Luisa Toscano, and Nina V. Zadoianchuk Regularity of Weak Solutions and Their Attractors for a Parabolic Feedback Control Problem // Set-Valued and Variational Analysis. 2013. DOI: 10.1007/s11228-013-0233-8
  • Nataliia V. Gorban, Oleksiy V. Kapustyan, Pavlo O. Kasyanov Uniform trajectory attractor for non-autonomous reaction–diffusion equations with Caratheodory’s nonlinearity // Nonlinear Analysis 98 (2014) 13–26, http://dx.doi.org/10.1016/j.na.2013.12.004
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Mikhail Z. Zgurovsky Optimality Conditions for Total-Cost Partially Observable Markov Decision Processes // 52nd IEEE Conference on Decision and Control, December 10-13, 2013. Florence, Italy, pp. 5716-5721
  • Michael Z. Zgurovsky,  Pavlo O. Kasyanov Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies // Continuous and Distributed Systems: Theory and Applications, Solid Mechanics and Its Applications, Volume 211, 2014, pp 149-162
  • Oleksiy V. Kapustyan,  Pavlo O. Kasyanov, José Valero, Mikhail Z. Zgurovsky Structure of Uniform Global Attractor for General Non-Autonomous Reaction-Diffusion System // Continuous and Distributed Systems: Theory and Applications, Solid Mechanics and Its Applications, Volume 211, 2014, pp 163-180.
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Mikhail Z. Zgurovsky Optimality Conditions for Partially Observable Markov Decision Processes// Continuous and Distributed Systems: Theory and Applications, Solid Mechanics and Its Applications, Volume 211, 2014, pp 251-264.
  • Gorban N.V., Kasyanov P.O., Kapustyan O.V., Palichuk L.S. On global attractors for autonomous wave equation with discontinuous nonlinearity // Solid Mechanics and Its Applications. – 2013. – vol. 211. – P. 221-237.
  • Pavlo O. Kasyanov, Luisa Toscano, Nina V. Zadoianchuk Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations // Solid Mechanics and Its Applications. – 2013. – vol. 211. – P. 181-187.
  • Gorban N.V., Kasyanov P.O. On Regularity of All Weak Solutions and Their Attractors for Reaction-Diffusion Inclusion in Unbounded Domain Equations // Solid Mechanics and Its Applications. – 2013. – vol. 211. – P. 205-220.
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Mark Voorneveld Berge’s maximum theorem for noncompact image sets // Journal of Mathematical Analysis and Applications, 413 (2014) 1040–1046, http://dx.doi.org/10.1016/j.jmaa.2013.12.011
  • Oleksiy V. Kapustyan, Pavlo O. Kasyanov, Jose Valero Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term // Discrete and Continuous Dynamical Systems, Volume 34, Number 10, October 2014, pp. 4155–4182 doi:10.3934/dcds.2014.34.4155
  • П. О. Касьянов, Л. С. Палийчук, А. Н. Ткачук, “Метод многозначных полугрупп операторов в исследовании долгосрочных прогнозов управляемых пьезоэлектрических полей”, Чебышевский сб., 15:2 (2014), 21–32
  • M.Z. Zgurovsky, P.O. Kasynov, L.S. Paliichuk Automatic Feedback Control for One  Class of Contact Piezoelectric Problems System Research & Information Technologies, 2014, № 1, 56-68
  • E. A. Feinberg, P. O. Kasyanov, N. V. Zadoianchuk, “Fatou's lemma for weakly converging probabilities”, ТВП, 58:4 (2013), 812–818 DOI: 10.4213/tvp4544
  • Oleksiy V. Kapustyan, Pavlo O. Kasyanov, Jose Valero Regular Solutions and Global Attractors for Reaction-Diffusion Systems without Uniqueness Communications on Pure and Applied Analysis, Volume 13, Number 5, 2014, pp. 1891-1906 doi:10.3934/cpaa.2014.13.1891
  • Michael Z. Zgurovsky and Pavlo O. Kasyanov Evolution Inclusions in Nonsmooth Systems with Applications for Earth Data Processing : Uniform Trajectory Attractors for Nonautonomous Evolution Inclusions Solutions with Pointwise Pseudomonotone Mappings in [D. Gao et al. (eds.), Advances in Global Optimization, Springer Proceedings in Mathematics & Statistics 95, 2015, pp 283-294] DOI 10.1007/978-3-319-08377-3_28
  • Касьянов П.О., Палійчук Л.С. Потраекторна поведінка класу керованих п’єзоелектричних полів з немонотонним потенціалом // Наукові вісті НТУУ «КПІ», 2014, №2, 21-27
  • Gluzman M.O., Gorban N.V., Kasyanov P.O. Lyapunov type functions for classes of autonomous parabolic feedback control problems and applications Applied Mathematics Letters, 2015. – Vol. 39. –P. 19-21, http://dx.doi.org/10.1016/j.aml.2014.08.006
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky Convergence of Probability Measures and Markov Decision Models with Incomplete Information, Proceedings of the Steklov Institute of Mathematics. - 2014. - Vol. 287. - P. 103–124
  • Eugene A. Feinberg, Pavlo O. Kasyanov Continuity of Minima: Local Results, Set-Valued and Variational Analysis, Vol. 23, 2015, pp. 485-499, DOI: 10.1007/s11228-015-0318-7
  • Feinberg, E.A., Kasyanov, P.O., Zgurovsky, M.Z. Convergence of value iterations for total-cost MDPs and POMDPs with general state and action sets, IEEE SSCI 2014 - 2014 IEEE Symposium Series on Computational Intelligence - ADPRL 2014: 2014 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning, Proceedings, 2014, pp. 1-8, DOI:10.1109/ADPRL.2014.7010613
  • Oleksiy V. Kapustyan, Pavlo O. Kasyanov, Jose Valero Structure of the Global Attractor for Weak Solutions of a Reaction-Diffusion Equation Applied Mathematics & Information Sciences, Vol. 9, No. 5, 2257-2264 (2015)http://dx.doi.org/10.12785/amis/090506
  • P. O. Kasyanov On the Existence of Strongly Continuous Physical Solutions for Classes of Autonomous Evolutionary Variational Inequalities, Cybernetics and Systems Analysis, July 2015, Volume 51, Issue 4, pp 574-582 DOI: 10.1007/s10559-015-9748-3
  • Mikhail Z. Zgurovsky, Pavlo O. Kasyanov Uniform Trajectory Attractors for Nonautonomous Dissipative Dynamical Systems Continuous and Distributed Systems II, Volume 30 of the series Studies in Systems, Decision and Control, 2015, pp 221-232, doi: 10.1007/978-3-319-19075-4_13
  • Mark O. Gluzman, Nataliia V. Gorban , Pavlo O. Kasyanov Lyapunov Functions for Differential Inclusions and Applications in Physics, Biology, and Climatology Continuous and Distributed Systems II, Volume 30 of the series Studies in Systems, Decision and Control, 2015, pp 233-243, doi: 10.1007/978-3-319-19075-4_14
  • Mikhail Z. Zgurovsky, Pavlo O. Kasyanov, Liliia S. Paliichuk , Alla M. Tkachuk Dynamics of Solutions for Controlled Piezoelectric Fields with Multivalued “Reaction-Displacement” Law Continuous and Distributed Systems II, Volume 30 of the series Studies in Systems, Decision and Control, 2015, pp 267-276, doi: 10.1007/978-3-319-19075-4_16
  • Mark O. Gluzman, Nataliia V. Gorban, Pavlo O. Kasyanov, Lyapunov Functions for Weak Solutions of Reaction-Diffusion Equations with Discontinuous Interaction Functions and its Applications, Nonautonomous Dynamical Systems. Volume 1, Issue 1, ISSN (Online) 2353-0626, DOI: 10.1515/msds-2015-0001, May 2015
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky Partially Observable Total-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities, Mathematics of Operations Research, 2016, doi: 10.1287/moor.2015.0746
  • O. V. Kapustyan, P. O. Kasyanov, J. Valero, A. Giménez, J. M. Amigó, Convergence of Numerical Approximations for a Non-Newtonian Model of Suspensions, International Journal of Bifurcation and Chaos, Vol. 25, Issue 14, 2015, doi: 10.1142/S0218127415400222
  • J. Valero, A. Giménez, O.V. Kapustyan, P.O. Kasyanov, J.M. Amigó, Convergence of equilibria for numerical approximations of a suspension model, Computers & Mathematics with Applications, 2016, doi:10.1016/j.camwa.2016.05.034
  • M.Z. Zgurovsky and P.O. Kasyanov, Uniform Global Attractors for Nonautonomous Evolution Inclusions, Springer International Publishing, Switzerland, 2016, V.A. Sadovnichiy and M.Z. Zgurovsky (eds.), Advances in Dynamical Systems and Control, Studies in Systems, Decision and Control 69, DOI 10.1007/978-3-319-40673-2_3
  • N.V. Gorban, M.O. Gluzman, P.O. Kasyanov and A.M. Tkachuk Long-time Behavior of State Functions for Badyko Models, Springer International Publishing, Switzerland, 2016, V.A. Sadovnichiy and M.Z. Zgurovsky (eds.), Advances in Dynamical Systems and Control, Studies in Systems, Decision and Control 69, DOI 10.1007/978-3-319-40673-2_18
  • Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky Uniform Fatou’s Lemma, Journal of Mathematical Analysis and Applications, 2016 (in press)