Seminars:
Computational mathematics Thu 16:15-17:45
room 1016 Image and Data Processing Tue 11:30-13:00
room 1146 Differential equations and related issues Fri 12:15-13:45
room 1016 Partial differential equations Tue 12:15-13:45
room 1016
Piotr Kalita, PhD
room:2147
address:Łojasiewicza 6, PL-30-348 Kraków, Poland
phone:(+48) 012 664 7538
e-mail:piotr.kalita At ii.uj.edu.pl
Research interests:
  • fluid mechanics
  • autonomous and nonautonomous infinite dimensional dynamical systems
  • partial differential equations of mathematical physics
  • multivalued dynamical systems and their attractors
  • differential inclusions and their application in contact mechanics
CV light:
2001M.Sc. in computer science Jagiellonian University (supervisor: Prof. Robert Schaefer)
2005PhD in computer science Jagiellonian University (supervisor: Prof. Robert Schaefer)
2016habilitation in mathematics Jagiellonian University
Awards and scholarships:
2005 Finalist in the selection process in the prize for best PhD thesis ECCOMAS (European Community on Computational Methods in Applied Sciences)
Books:
  • G. Łukaszewicz, P. Kalita,
    Navier-Stokes equations. An introduction with applications
    Advances in Mechanics and Mathematics, vol. 34, Springer, 2016
Publications:
  1. Juan Garcia-Fuentes, Piotr Kalita, Jose A. Langa, Antonio Suarez,
    Forwards attractors for non-autonomous Lotka-Volterra cooperative systems: a detailed geometrical description
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 30, 189-221 (2025)
  2. Jakub Banaśkiewicz, Piotr Kalita, Piotr Zgliczyński,
    Computer-assisted validation of the existence of periodic orbit in the Brusselator system
    Advances in Differential Equations, vol. 29, 815-862 (2024)
  3. Piotr Kalita, Everaldo de Mello Bonotto,
    Long-time behavior for impulsive generalized semiflows
    Nonlinear Analysis-Hybrid Systems, vol. 51, 101432 (2024)
  4. Juan Garcia-Fuentes, Piotr Kalita, Jose A. Langa,
    Forwards attractor structures in a planar cooperative non-autonomous Lotka-Volterra system
    Qualitative Theory of Dynamical Systems, vol. 23, article number 163 (2024)
  5. Jakub Banaśkiewicz, Alexandre Nolasco de Carvalho, Juan Garcia-Fuentes, Piotr Kalita,
    Autonomous and non-autonomous unbounded attractors in evolutionary problems
    Journal of Dynamics and Differential Equations, vol. 36, 3481-3534 (2024)
  6. Matheus Cheque Bortolan, Juliana Fernandes, Juan Garcia-Fuentes, Piotr Kalita,
    On maximal attractors for dynamical systems. Application to a semilinear parabolic problem with controlled growth
    JOURNAL OF EVOLUTION EQUATIONS, vol. 24, Article number 38 (2024)
  7. Pablo Almaraz, Piotr Kalita, Jose A. Langa, Fernando Soler-Toscano,
    Structural stability of invasion graphs for Lotka-Volterra systems
    JOURNAL OF MATHEMATICAL BIOLOGY, vol. 88, article number 64 (2024)
  8. Ruben Caballero Toro, Piotr Kalita, Jose Valero Cuadra,
    On $L^{\infty}$-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, available online (2024)
  9. Jakub Banaśkiewicz, Piotr Kalita,
    Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation
    APPLIED MATHEMATICS AND OPTIMIZATION, vol. 84, 943-978 (2021)
  10. Anna Denkowska, Piotr Gwiazda, Piotr Kalita,
    On renormalized solutions to elliptic inclusions with nonstandard growth
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, vol. 60, Article number: 21 (2021)
  11. Piotr Kalita, Piotr Zgliczyński,
    Rigorous FEM for 1D Burgers Equation
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 20, 853–907 (2021)
  12. Piotr Kalita, Piotr Zgliczyński,
    On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION AMATHEMATICS, vol. 150, 2025-2054 (2020)
  13. Everaldo de Mello Bonotto, Piotr Kalita,
    On attractors of generalized semiflows with impulses
    JOURNAL OF GEOMETRIC ANALYSIS, vol. 30, 1412-1449 (2020)
  14. Leszek Gasiński, Piotr Kalita,
    On dynamic contact problem with generalized Coulomb friction, normal compliance and damage
    Evolution Equations and Control Theory, vol. 9, 1009-1026 (2020)
  15. Piotr Kalita, Grzegorz Łukaszewicz,
    Micropolar meets Newtonian in 3D. The Rayleigh-Bénard problem for large Prandtl numbers
    NONLINEARITY, vol. 33, 5686 (2020)
  16. Piotr Kalita, Grzegorz Łukaszewicz, Jakub Siemianowski,
    Nonlinear Semigroups and Their Perturbations in Hydrodynamics. Three Examples
    Springer, vol. 325, 227-250 (2020)
  17. Matteo Caggio, Piotr Kalita, Grzegorz Łukaszewicz, Krzysztof Mizerski,
    Vertical heat transport at infinite Prandtl number for micropolar fluid
    ARCHIVES OF MECHANICS, vol. 72, 525-553 (2020)
  18. Piotr Kalita, Jose A. Langa, Grzegorz Łukaszewicz,
    Micropolar meets Newtonian. The Rayleigh–Bénard problem
    PHYSICA D-NONLINEAR PHENOMENA, vol. 392, 57-80 (2019)
  19. Piotr Kalita, Jose A. Langa, Fernando Soler-Toscano,
    Informational Structures and Informational Fields as a prototype for the description of postulates of the Integrated Information Theory
    ENTROPY-SWITZ, vol. 21, 493 (2019)
  20. Piotr Kalita, Grzegorz Łukaszewicz, Jakub Siemianowski,
    On relation between attractors for single and multivalued semiflows for a certain class of PDEs
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 24, 1199-1227 (2019)
  21. Piotr Kalita, Meir Shillor, Paweł Szafraniec,
    A frictional contact problem with wear diffusion
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, vol. 70, 96 (2019)
  22. Mikael Barboteu, Leszek Gasiński, Piotr Kalita,
    Analysis of a dynamic frictional contact problem for hyperviscoelastic material with non-convex energy density
    MATHEMATICS AND MECHANICS OF SOLIDS, vol. 23, 359-391 (2018)
  23. Mirelson M. Freitas, Piotr Kalita, Jose A. Langa,
    Continuity of non-autonomous attractors for hyperbolic perturbation of parabolic equations
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 264, 1886-1945 (2018)
  24. Piotr Kalita, Grzegorz Łukaszewicz, Jakub Siemianowski,
    Rayleigh-Benard problem for Thermomicropolar Fluids
    Topological Methods in Nonlinear Analysis, vol. 52, 477-514 (2018)
  25. Piotr Kalita, Piotr Kowalski,
    On multivalued Duffing equation
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 462, 1130-1147 (2018)
  26. Robert Filipek, Piotr Kalita, Lucjan Sapa, Krzysztof Szyszkiewicz,
    On local weak solutions to Nernst–Planck–Poisson system
    APPLICABLE ANALYSIS, vol. 96, 2316-2332 (2017)
  27. Sylwia Dudek, Piotr Kalita, Stanisław Migórski,
    Stationary Oberbeck-Boussinesq model of generalized Newtonian fluid governed by multivalued partial differential equations
    APPLICABLE ANALYSIS, vol. 96, 2192-2217 (2017)
  28. Sylwia Dudek, Piotr Kalita, Stanisław Migórski,
    Steady flow of generalized Newtonian fluid with multivalued rheology and nonmonotone friction law
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 74, 1813-1825 (2017)
  29. Michele Coti Zelati, Piotr Kalita,
    Smooth attractors for weak solutions of the SQG equation with critical dissipation
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 22, 1857-1873 (2017)
  30. S. Dudek, P. Kalita, S. Migórski,
    Stationary Oberbeck–Boussinesq model of non-Newtonian ?uid governed by a system of multivalued partial differential equations
    Applicable Analysis, 96, 2192-2217 (2017)
  31. Piotr Kalita,
    On Global Attractor for Parabolic Partial Differential Inclusion and Its Time Semidiscretization
    Springer, 35-64 (2016)
  32. Piotr Kalita, Stanisław Migórski, Mircea Sofonea ,
    A multivalued variational inequality with unilateral constraints
    Springer, vol. 494, 302-312 (2016)
  33. Leszek Gasiński, Piotr Kalita,
    On quasi-static contact problem with generalized Coulomb friction, normal compliance and damage
    EUROPEAN JOURNAL OF APPLIED MATHEMATICS, vol. 27, 625-646 (2016)
  34. Krzysztof Bartosz, Piotr Kalita, Stanisław Migórski, Anna Ochal, Mircea Sofonea,
    History dependent problems with applications to contact models for elastic beams
    APPLIED MATHEMATICS AND OPTIMIZATION, vol. 73, 71-98 (2016)
  35. Piotr Kalita, Grzegorz Łukaszewicz,
    Navier-Stokes Equations. An introduction with applications
    Springer, (2016)
  36. Piotr Kalita, Stanisław Migórski, Mircea Sofonea ,
    A class of subdifferential inclusions for elastic unilateral contact problems
    Set-Valued and Variational Analysis, vol. 24, 355-379 (2016)
  37. Jose Ramon Fernandez, Piotr Kalita, Stanisław Migórski, Maria del Carmen Muniz, Cristina Nunez,
    Existence and uniqueness results for a kinetic model in bulk-surface surfactant dynamics
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 48, 3065-3089 (2016)
  38. Andrzej Bielecki, Maciej Gierdziewicz, Piotr Kalita, Kamil Szostek,
    Construction of a 3D geometric model of a presynaptic bouton for use in modeling of neurotransmitter flow
    LECTURE NOTES IN COMPUTER SCIENCE, vol. 9972, 377-386 (2016)
  39. Jerzy Czepiel, Piotr Kalita,
    Numerical solution of a variational-hemivariational inequality modeling simplified adhesion of an elastic body
    IMA JOURNAL OF NUMERICAL ANALYSIS, vol. 35, 372-393 (2015)
  40. Mikael Barboteu, Krzysztof Bartosz, Piotr Kalita, Ahmad Ramadan,
    A Contact Problem with Normal Compliance, Finite Penetration and Nonmonotone Slip Dependent Friction
    Springer Verlag (połaczony z Kluwer Academic Publishing), vol. 95, 295-303 (2015)
  41. Mikael Barboteu, Krzysztof Bartosz, Piotr Kalita,
    A dynamic viscoelastic contact problem with normal compliance, finite penetration and nonmonotone slip rate dependent friction
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, vol. 22, 452-472 (2015)
  42. Piotr Kalita, Grzegorz Łukaszewicz,
    On Large Time Asymptotics for Two Classes of Contact Problems
    Springer, vol. 33, 299-332 (2015)
  43. Krzysztof Bartosz, Xiaoliang Cheng, Piotr Kalita, Yuanjie Yu, Cong Zeng,
    Rothe method for parabolic variational-hemivariational inequalities
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 423, 841-862 (2015)
  44. Krzysztof Bartosz, Zdzisław Denkowski, Piotr Kalita,
    Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions
    APPLIED MATHEMATICS AND OPTIMIZATION, vol. 71, 379-410 (2015)
  45. Piotr Kalita, Grzegorz Łukaszewicz,
    Attractors for multivalued processes with weak continuity properties
    Springer, 149-166 (2015)
  46. Michele Coti Zelati, Piotr Kalita,
    Minimality properties of set-valued processes and their pullback attractors
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 47, 1530-1561 (2015)
  47. Sylwia Dudek, Piotr Kalita, Stanisław Migórski,
    Stationary flow of non–Newtonian fluid with nonmonotone frictional boundary conditions
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, vol. 66, 2625-2646 (2015)
  48. Jose Ramon Fernandez, Piotr Kalita, Stanisław Migórski, Maria del Carmen Muniz, Cristina Nunez,
    Variational analysis of the Langmuir–Hinshelwood dynamic mixed-kinetic adsorption model
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, vol. 15, 205–220 (2014)
  49. Mikael Barboteu, Krzysztof Bartosz, Piotr Kalita, Ahmad Ramadan,
    Analysis of a contact problem with normal compliance, finite penetration and nonmonotone slip dependent friction
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 16, 1350016 [29 pages] (2014)
  50. Piotr Kalita, Grzegorz Łukaszewicz,
    Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, vol. 19, 75-88 (2014)
  51. Piotr Kalita, Grzegorz Łukaszewicz,
    Global attractors for multivalued semiflows with weak continuity properties
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol. 101, 124-143 (2014)
  52. Piotr Kalita,
    Convergence of Rothe scheme for hemivariational inequalities of parabolic type
    International Journal of Numerical Analysis and Modeling, vol. 10, 445-465 (2013)
  53. Mikael Barboteu, Krzysztof Bartosz, Piotr Kalita,
    An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
    International Journal of Applied Mathematics and Computer Science, vol. 23, 263-276 (2013)
  54. Jose Ramon Fernandez, Piotr Kalita, Stanisław Migórski, Maria del Carmen Muniz, Cristina Nunez,
    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, 601-614 (2013)
  55. M. Barboteu, K. Bartosz, P. Kalita,
    Analysis and numerical approach to a bilateral contact problem with nonmonotone friction
    International Journal of Applied Mathematics and Computer Science, 23, 263-276 (2013)
  56. Krzysztof Bartosz, Piotr Kalita,
    Optimal control for a class of dynamic viscoelastic contact problems with adhesion
    DYNAMIC SYSTEMS AND APPLICATIONS, vol. 21, 269-292 (2012)
  57. Piotr Kalita,
    Regularity and Rothe method error estimates for parabolic hemivariational inequality
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 389, 618-631 (2012)
  58. Andrzej Bielecki, Piotr Kalita,
    Dynamical properties of the reaction-diffusion type model of fast synaptic transport
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 393, 329–340 (2012)
  59. Piotr Kalita,
    Decay of energy for second-order boundary hemivariational inequalities with coercive damping
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol. 74, 1164-1181 (2011)
  60. A. Bielecki, P. Kalita, M. Lewandowski, B. Siwek,
    Numerical simulation for neurotransmitter transport model in axon terminal of presynaptic neuron
    Biological Cybernetics, 102, 489-502 (2010)
  61. Andrzej Bielecki, Piotr Kalita, Marian Lewandowski, Bartłomiej Siwek,
    Numerical simulation for a neurotransmitter transport model in the axon terminal of a presynaptic neuron
    BIOLOGICAL CYBERNETICS, vol. 102, 489-502 (2010)
  62. Andrzej Bielecki, Piotr Kalita,
    Model of neurotransmitter fast transport in axon terminal of presynaptic neuron
    JOURNAL OF MATHEMATICAL BIOLOGY, vol. 56, 559-576 (2008)
  63. Bartosz Bierkowski, Piotr Kalita, Igor Podolak, Adam Roman,
    Algorithm for intelligent prediction of requests in business systems
    LECTURE NOTES IN COMPUTER SCIENCE, vol. 4910, 696-707 (2008)
  64. Andrzej Bielecki, Piotr Kalita, Marian Lewandowski, Marek Skomorowski,
    Compartment model of neuropeptide synaptic transport with impulse control
    BIOLOGICAL CYBERNETICS, vol. 99, 443-458 (2008)
  65. Piotr Kalita, Robert Schaefer,
    Mechanical models of artery walls
    ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, vol. 15, 1-36 (2008)
Division of Computational Mathematics, Institute of Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland