Chair of Optimization and Control

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. 2148

Phone: 48 12 664 7537

Fax: 48 12 664 6673

Email: krzysztof.bartosz(at)ii.uj.edu.pl, bartosz(at)ii.uj.edu.pl

Office hours: Tuesday    14.00-15.00
                      Thursday  12.30-13.30

Theory of Sobolev spaces, partial differential equations, variational and hemivariational inequalities, mechanics of solids concerning elasticity and viscosity properties of material and nonmonotone contact conditions, optimal control and numerical solving of the above problems, Rothe method, Galerkin method, Finite Element Method, computer simulations.

• Studied Mathematics 1998-2003, AGH University of Science and Technology, Krakow
• Master of Science in Mathematics 2003, AGH University of Science and Technology
• PhD in Mathematics 2007, Jagiellonian University
• Habilitation in Mathematics 2018, Jagiellonian University

1. P. Bartman, K. Bartosz, M. Jureczka, P. Szafraniec, Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem, Nonlinear Analysis: Real World Applications, (2023), https://doi.org/10.1016/j.nonrwa.2023.103870
2. K. Bartosz, P. Szafraniec, J. Zhao, Convergence of a double step scheme for a class of parabolic Clarke subdifferential inclusions, Communications in Nonlinear Science and Numerical Simulation, (2021), https://doi.org/10.1016/j.cnsns.2021.105940
3. M. Barboteu, K. Bartosz, D. Danan, Analysis of a dynamic contact problem with nonmonotone friction and non clamped boundary conditions, Applied Numerical Mathematics vol. 126 (2018), 53-77, https://doi.org/10.1016/j.apnum.2017.12.005
4. K. Bartosz, T. Janiczko, P. Szafraniec, M. Shillor, Dynamic thermoviscoelastic thermistor problem with contact and nonmonotone friction, Applicable Analysis, vol. 97:8 (2018), 1432-1453, http://dx.doi.org/10.1080/00036811.2017.1403586
5. K. Bartosz, M. Sofonea, Subdifferential inclusions for stress formulations of unilateral contact problems, Mathematics and Mechanics of Solids, vol. 23:3 (2018) 392–410, http://journals.sagepub.com/doi/pdf/10.1177/1081286517709518
6. K. Bartosz, L. Gasiński, Z. Liu, P. Szafraniec, Convergence of a time discretization for nonlinear second order inclusion, Proceedings of the Edinburgh Mathematical Society, 61:1 (2018), 93-120, https://doi.org/10.1017/S0013091516000560
7. K. Bartosz, Convergence of Rothe scheme for a class of dynamic variational inequalities involving Clarke subdifferential, Applicable Analysis, vol. 97:13 (2018), 2189-2209, http://dx.doi.org/10.1080/00036811.2017.1359562
8. K. Bartosz, Variable time-step theta-scheme for nonlinear second order evolution inclusion, International Journal of Numerical Analysis and Modeling, vol. 14:6 (2017), 842-868, http://www.math.ualberta.ca/ijnam/Volume-14-2017/No-6-17/2017-06-03.pdf
9. M. Barboteu, K. Bartosz, W. Han, Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics, Computer Methods in Applied Mechanics and Engineering, vol. 318 (2017), 882-897, https://doi.org/10.1016/j.cma.2017.02.003
10. K. Bartosz, M. Sofonea, A dynamic contact model for viscoelastic plates, Quarterly Journal of Mechanics and Applied Mathematics, vol. 70 (2017), 1-19, https://doi.org/10.1093/qjmam/hbw013
11. K. Bartosz, D. Danan, P. Szafraniec, Numerical analysis of a dynamic bilateral thermoviscoelastic contact problem with nonmonotone friction law, Computers and Mathematics with Applications, vol. 73 (2017), 727-746, https://doi.org/10.1016/j.camwa.2016.12.026
12. 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, vol. 73 (2016), 71-98, https://link.springer.com/article/10.1007/s00245-015-9292-6
13. K. Bartosz, M. Sofonea, The Rothe Method for Variational-Hemivariational Inequalities with applications to Contact Mechanics, SIAM Journal on Mathematical Analysis, vol. 48:22 (2016), 861-883,  https://doi.org/10.1137/151005610
14. K. Bartosz, M. Sofonea, Modeling and analysis of a contact problem for a viscoelastic rod, Zeitshrift fur Angewandte Mathematik und Physik, vol. 67:127 (2016), 21 pages, https://link.springer.com/article/10.1007/s00033-016-0718-z
15. M. Barboteu, K. Bartosz, T. Janiczko, W. Han, Numerical analysis of a hyperbolic hemivariational inequality arising in dynamic contact, SIAM Journal of Numerical Analysis, vol. 53:1 (2015), 527-550, https://doi.org/10.1137/140969737
16. K. Bartosz, Z. Denkowski, P. Kalita, Sensitivity of optimal solutions to control problems for second order evolution subdifferential inclusions, Applied Mathematics and Optimization, vol. 71 (2015), 379-410, https://link.springer.com/article/10.1007/s00245-014-9262-4
17. K. Bartosz, X. Cheng, P. Kalita, Y. Yu. C. Zeng, Rothe method for parabolic variational-hemivariational inequalities, Journal of Mathematical Analysis and Applications, vol. 423 (2015), 841-862, https://doi.org/10.1016/j.jmaa.2014.09.078
18. K. Bartosz, P. Kalita, M. Barboteu, A dynamic viscoelastic contact problem with normal compliance, finite penetration and nonmonotone slip rate dependent friction, Nonlinear Analysis: Real World Applications, vol. 22 (2015), 452-472, https://doi.org/10.1016/j.nonrwa.2014.08.009
19. 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, vol. 16:1 (2014), 1350016 [29 pages], https://doi.org/10.1142/S0219199713500168
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, vol. 23 (2013), 263-276, https://doi.org/10.2478/amcs-2013-0020
21. K. Bartosz, P. Kalita, Optimal control for a class of dynamic viscoelastic contact problems with adhesion, Dynamic Systems and Applications, vol. 21 (2012), 269-292.
22. K. Bartosz, Hemivariational Inequalities Modeling Dynamic Contact Problems with Adhesion, Nonlinear Analysis, Theory, Methods and Applications vol. 71 (2009) 1747-1762, https://doi.org/10.1016/j.na.2009.01.011
23. K. Bartosz, Hemivariational Inequality Approach to the Dynamic Viscoelastic Sliding Contact Problem with Wear, Nonlinear Analysis, Theory, Methods and Applications vol. 65 (2006) 546-566, https://doi.org/10.1016/j.na.2005.09.027

Book chapters

1. K. Bartosz, Numerical Methods for Evolution Hemivariational Inequalities, in: Advances in Variational and Hemivariational Inequalities, Advances in Mechanics and Mathematics, vol. 33, W. Han, S. Migórski, M. Sofonea (eds.), Springer 2015, 109-142.
2. 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.