Optimization and Control @ Jagiellonian University

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Members

Krzysztof Bartosz

Marcin Ciecholewski

Jacek Cyranka

Zdzisław Denkowski

Maria Foryś

Leszek Gasiński

Piotr Kalita

Anna Kulig

Stanisław Migórski

Anna Ochal

Seminars

Maestro Seminar

Wed. 10:15-13:45

Modeling, Optimization and Control

Thu. 10:15-11:45

Partial Differential Equations

Tue. 12:15-13:45

Software Engineering and Related Topics

Wed. 12:15-13:45

Marie Curie projects

FP7 People CONTACT Project

Maestro Advanced Project

Piotr Kalita

dr hab. Piotr Kalita, PhD

Address

Jagiellonian University

Faculty of Mathematics and Computer Science

ul. Lojasiewicza 6, PL-30348 Kraków

Office

Institute of Computer Science

ul. Lojasiewicza 6, PL-30348 Kraków

Office no. 2147

Phone: 48 12 664 7538

Fax: 48 12 664 6673

Email: piotr.kalita(at)ii.uj.edu.pl, kalita(at)ii.uj.edu.pl

Office hours: Tuesdays: 17.45-18.45, Wednesdays: 14.15-15.15.

Main interests

fluid mechanics; multivalued dynamical systems; infinite dimensional dynamical systems; variational inlusions and inequalities; asymptotic behavior of solutions; convergence analysis and implementation of numerical methods; contact problems of mechanics; mathematical modeling in biology

Curriculum vitae

Studied Computer Science 1996-2001, Jagiellonian University

Master of Science in Computer Science, 2001, Jagiellonian University

PhD in Computer Science, 2005, Jagiellonian University

Habilitation in Mathematics, 2016, Jagiellonian University

Publications

Book

  1. G. Łukaszewicz, P. Kalita, Navier--Stokes equations. An introduction with applications, Advances in Mechanics and Mathematics, vol. 34, Springer, 2016, DOI: 10.1007/978-3-319-27760-8 link

Submitted papers

  1. L. Gasiński, P. Kalita, On dynamic contact problem with generalized Coulomb friction, normal compliance and damage
  2. P. Kalita, P. Kowalski, On multivalued Duffing equation

Research papers in journals

  1. M. Coti Zelati, P. Kalita, Smooth attractors for weak solutions of the SQG equation with critical dissipation, to appear in Discrete and Continuous Dynamical Systems Series B, 22 (2017), 1857-1873, DOI: 10.3934/dcdsb.2017110
  2. S. Dudek, P. Kalita, S. Migórski, Steady flow of generalized Newtonian fluid with multivalued rheology and nonmonotone friction law, to appear in Computers and Mathematics with Applications
  3. R. Filipek, P. Kalita, L. Sapa, K. Szyszkiewicz, On local weak solutions to Nernst–Planck–Poisson system, to appear in Applicable Analysis, DOI: 10.1080/00036811.2016.1221941
  4. S. Dudek, P. Kalita, S. Migórski, Stationary Oberbeck–Boussinesq model of non-Newtonian fluid governed by a system of multivalued partial differential equations, to appear in Applicable Analysis, DOI: 10.1080/00036811.2016.1209743
  5. J.R. Fernández, P. Kalita, S. Migórski, M.C. Muñiz, C. Núñez, Existence and uniqueness results for a kinetic model in bulk-surface surfactant dynamics, SIAM Journal on Mathematical Analysis, 48 (2016), 3065-3089, DOI: 10.1137/15M1012785
  6. A. Bielecki, M. Gierdziewicz, P. Kalita, K. Szostek, Construction of a 3D geometric model of a presynaptic bouton for use in modeling of neurotransmitter flow, Lecture Notes in Computer Science, 9972, 2016, 377-386, DOI: 10.1007/978-3-319-46418-3_33.
  7. L. Gasiński, P. Kalita, On quasistatic contact problem with generalized Coulomb friction, normal compliance and damage, European Journal of Applied Mathematics, 27 (2016), 625--646, DOI: 10.1017/S0956792515000583
  8. P. Kalita, S. Migórski, M. Sofonea, A class of subdifferential inclusions for elastic unilateral contact problems, Set-Valued and Variational Analysis, 24 (2016), 355--379, DOI: 10.1007/s11228-015-0346-3
  9. K. Bartosz, P. Kalita, S. Migórski, A. Ochal, M. Sofonea, History-dependent problems with applications to contact models for elastic beams, Applied Mathematics and Optimization, 73 (2016), 71-98, DOI: 10.1007/s00245-015-9292-6
  10. S. Dudek, P. Kalita, S. Migórski, Stationary flow of non-Newtonian fluid with nonmonotone frictional boundary conditions, Zeitschrift für angewandte Mathematik und Physik, 66 (2015), 2625-2646, DOI: 10.1007/s00033-015-0545-7
  11. M. Coti Zelati. P. Kalita, Minimality properties of set-valued processes and their pullback attractors, SIAM Journal on Mathematical Analysis, 47 (2015), 1530-1561, DOI: 10.1137/140978995
  12. M. Barboteu, K. Bartosz, P. Kalita, A dynamic viscoelastic contact problem with normal compliance, finite penetration and nonmonotone slip rate dependent friction, Nonlinear Analysis: Real World Applications, 22 (2015), 452-472, DOI: 10.1016/j.nonrwa.2014.08.009.
  13. K. Bartosz, X. Cheng, P. Kalita, Y. Yu. C. Zheng, Rothe method for parabolic variational-hemivariational inequalities, Journal of Mathematical Analysis and Applications, 423 (2015), 841-862, DOI: 10.1016/j.jmaa.2014.09.078.
  14. K. Bartosz, Z. Denkowski, P. Kalita, Sensitivity of optimal solutions to control problems for second order evolution subdifferential inclusions, Applied Mathematics and Optimization, 71 (2015), 379-410, DOI: 10.1007/s00245-014-9262-4
  15. J. Czepiel, P. Kalita, Numerical solution of a variational-hemivariational inequality modeling simplified adhesion of an elastic body, IMA Journal of Numerical Analysis, 35 (2015), 372-393, DOI: 10.1093/imanum/drt058.
  16. P. Kalita, G. Łukaszewicz, Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions, Nonlinear Analysis: Real World Applications, 19 (2014), 75-88, DOI : 10.1016/j.nonrwa.2014.03.002
  17. P. Kalita, G. Łukaszewicz, Global attractors for multivalued semiflows with weak continuity properties, Nonlinear Analysis Series A, Theory, Methods & Applications, 101 (2014), 124-143.
  18. M. Barboteu, K. Bartosz, P. Kalita, A. Ramadan, Analysis of a contact problem with normal compliance, finite penetration and nonmonotone slip dependent friction, Communications in Contemporary Mathematics, 16 (2014), 1350016 [29 pages], DOI: 10.1142/S0219199713500168
  19. J.R. Fernández, P. Kalita, S. Migórski, M.C. Muñiz, C. Núñez, Variational analysis of the Langmuir-Hinshelwood dynamic mixed-kinetic adsorption model, Nonlinear Analysis: Real World Applications, 15 (2014), 205-220, DOI: 10.1016/j.nonrwa.2013.07.005.
  20. M. Barboteu, K. Bartosz, P. Kalita, An analytical and numerical approach to a bilateral contact problem with nonmonotone friction, International Journal of Applied Mathematics and Computer Science, 23 (2013), 263-276.
  21. P. Kalita, Convergence of Rothe scheme for hemivariational inequalities of parabolic type, International Journal of Numerical Analysis & Modeling, 10 (2013), 445-465.
  22. A. Bielecki, P. Kalita, Dynamical properties of the reaction-diffusion type model of fast synaptic transport, Journal of Mathematical Analysis and Applications, 393 (2012), 329–340.
  23. K. Bartosz, P. Kalita, Optimal control for a class of dynamic viscoelastic contact problems with adhesion, Dynamic Systems and Applications, 21 (2012), 269-292.
  24. P. Kalita, Regularity and Rothe method error estimates for parabolic hemivariational inequality, Journal of Mathematical Analysis and Applications, 389 (2012), 618-631.
  25. P. Kalita, Decay of energy for second-order boundary hemivariational inequalities with coercive damping, Nonlinear Analysis: Theory, Methods & Applications, 74 (2011), 1164-1181.
  26. A. Bielecki, P. Kalita, M. Lewandowski, B. Siwek, Numerical simulation for a neurotransmitter transport model in the axon terminal of a presynaptic neuron, Biological Cybernetics 102 (2010), 489-502.
  27. P. Kalita, A. Roman, I. Podolak, B. Bierkowski, Algorithm for intelligent prediction of requests in business systems, Lecture Notes in Computer Science, 4910 (2008), 696-707.
  28. A. Bielecki, P. Kalita, M. Lewandowski, M. Skomorowski, Compartment model of neuropeptide synaptic transport with impulse control, Biological Cybernetics, 99 (6) (2008), 443-458.
  29. P. Kalita, R. Schaefer, Mechanical models of artery walls, Archives of Computational Methods in Engineering, 15 (1) (2008), 1-36.
  30. A. Bielecki, P. Kalita, Model of neurotransmitter fast transport in axon terminal of presynaptic neuron, Journal of Mathematical Biology, 56 (4) (2008), 559-576.
  31. M. Paszyński, P. Kalita, R. Schaefer, The dynamics of human central arterial system, Schedae Informaticae, 14 (2005), 35-59.
  32. P. Kalita, Koiter shell governed by strongly monotone constitutive equations, International Journal of Applied Mathematics and Computer Science, 14 (2) (2004), 127-137.
  33. P. Kalita, Shell models of the artery wall, Schedae Informaticae, 13 (2004), 103-122.
Book chapters
  1. P. Kalita, S. Migórski, M. Sofonea, A multivalued variational inequality with unilateral constraints, to appear as a chapter in System Modeling and Optimization, IFIP Advances in Information and Communication Technology, L. Bociu et al. (eds.), Springer 2016, DOI: 10.1007/978-3-319-55795-3_28.
  2. P. Kalita, On global attractor for parabolic partial differential inclusion and its time semi-discretization, to appear as a chapter in: Advances in Mathematical Modeling, Optimization and Optimal Control, Springer Optimization and Its Applications vol. 109, J.-B. Hiriart-Urruty, A. Korytowski, H. Maurer, M. Szymkat (eds.), Springer 2016, DOI: 10.1007/978-3-319-30785-5_3 link
  3. P. Kalita, G. Łukaszewicz, Attractors for multivalued processes with weak continuity properties, in: Continuous and Distributed Systems II Theory and Applications, Studies in Systems, Decision and Control, vol. 30, V.A. Sadovnichiy, M.Z. Zgurovsky (eds.), Springer 2015, 149-166, DOI: 10.1007/978-3-319-19075-4_9.
  4. P. Kalita, G. Łukaszewicz, On Large Time Asymptotics for Two Classes of Contact Problems, in: Advances in Variational and Hemivariational Inequalities, Advances in Mechanics and Mathematics, vol. 33, W. Han, S. Migórski, M. Sofonea (eds.), Springer 2015, 299-332.
  5. A. Ramadan, M. Barboteu, K. Bartosz, P. Kalita, A Contact Problem with Normal Compliance, Finite Penetration and Nonmonotone Slip Dependent Friction, in: Advances in Global Optimization, Springer Proceedings in Mathematics & Statistics, vol. 95, D. Gao, N. Ruan, W. Xing (eds.), Springer, 2015, 295-303, doi: 10.1007/978-3-319-08377-3_29.
Research papers in peer reviewed post conference publications
  1. J.R. Fernández, P. Kalita, S. Migorski, M.C. Muñiz, C. Núñez, Variational and numerical analysis of a mixed kinetic-diffusion surfactant model for the modified the Langmuir-Hinshelwood equation, Proceedings of the 13th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2013, Almeria, Spain, June 24-27, 2013, vol. II, 601-614.
  2. A. Bielecki, P. Kalita, B. Siwek, Numerical method for simulation of the presynaptic episode of synaptic transmission, 18th International Conference on Computer Methods in Mechanics CMM 2009, Short Papers, Zielona Góra, 2009, p.119-120.
  3. P. Kalita, R. Schaefer, M. Paszyński, Nonlinear Models of Artery Dynamics, in: Mathematical Methods in Scattering Theory and Biomedical Engineering, Proceedings of 7th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, 8-11 September 2005, D.I. Fotiadis, C.V. Massalas (eds), World Scientific, New Jersey, London, 2006, 320-334.
  4. A. Bielecki, P. Kalita, M. Lewandowski, Model of fast synaptic transmission, Proceedings of XII National Conference on Application of Mathematics in Biology and Medicine, 26-29 September 2006, Koninki, Poland, 2006, 13-18.
  5. P. Kalita, R. Schaefer, Dynamics of the weakly nonlinear Koiter shell, in: Shell Structures: Theory and Applications, Proceedings of 8th Conference on Shell Structures Theory and Applications SSTA 2005, 11-15 October 2005, W. Pietraszkiewicz, C. Szymczak (eds), Taylor & Francis Group/Balkema, London, 2005, 125-128.
  6. P. Kalita, Artery wall modeling - a challenge for computer science and mathematics, in: Recent Developments in Artificial Intelligence Methods, Proceedings of Symposium on Methods of Artificial Intelligence AI-METH 2004, 17-19 November 2004, T. Burczyński, W. Cholewa, W. Moczulski (eds), Gliwice, Poland, 2004, 147-150.
  7. M. Paszyński, R. Schaefer, P. Kalita, Pulsative flows in large vessels (Przepływy pulsacyjne w dużych tętnicach), Proceedings of the Metody i Systemy Komputerowe MSK'03 Symposium, 26-28 November 2003, R. Tadeusiewicz, A. Ligęza, M. Szymkat (eds), Kraków, Poland, 2003, 129-134 (in Polish).
  8. P. Kalita, Arterial wall modeled by physically nonlinear Koiter shell, Proceedings of 15th International Conference on Computer Methods in Mechanics CMM-2003, 3-6 June 2003, Gliwice/Wisła, Poland, 2003, Published on Conference CD.
  9. P. Kalita, M. Paszyński, A. Pelc, Simulation of the initiation of pulse wave in the ascending aorta with the connected use of FPM and FEM, Proceedings of VIII National Conference on Application of Mathematics in Biology and Medicine, 25-28 September 2002, Łajs, Poland, 2002, 63–68.
  10. A. Kabała. P. Kalita. Application of thin shell theory for modeling dynamics of arterial walls, Proceedings of VII National Conference on Application of Mathematics in Biology and Medicine, 25-28 September 2001, Zawoja, Poland, 2001, 79-84.

Teaching

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Chair of Optimization and Control, Institute of Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland