Nonlinear Differential Variational-Hemivariational Inequalities with Applications

Dissemination of Results - Research Project Outcomes:

Conference / Symposium

Members of the research team presented the results obtained during the execution of the research tasks of the project at international conferences and seminars:
• A. Ochal, "Penalty method in the study of elliptic variational inequalities", Online seminar IMDETA (International Meetings on Differential Equations and Their Applications), December 3, 2025
• P. Bartman-Szwarc, "Dynamic Membrane Obstacle Problems with the Damped Normal Compliance Condition", The 26th International Conference on Computer Methods in Mechanics, Lodz, Poland, July 8-11, 2025
• K. Bartosz, "Vanishing viscosity method for a noncoercive hyperbolic differential hemivariational inequality”, 26th International Conference on Computer Methods in Mechanics, Łódź, Poland, July 8-11, 2025
• P. Bartman-Szwarc, "Hybrid Subgradient and Simulated Annealing Method for solving Hemivariational Inequalities", Symposium on Recent Progress in Nonlinear Problems: Theory, Computation & Applications, Southwest Petroleum University Xindu District, Chengdu, China, June 13-15, 2025
• K. Bartosz, "Existence of a weak solution for a dynamic adhesive Signorini's contact problem", Symposium on Recent Progress in Nonlinear Problems: Theory, Computation & Applications, Southwest Petroleum University Xindu District, Chengdu, China, June 13-15, 2025
• S. Migórski, invited talk "Navier-Stokes-Darcy hemivariational inequality", The 3rd Conference on Recent Advances in Nonlinear Problems: Theory, Computation, and Applications, Southwest Petroleum University Xindu District, Chengdu, China, June 13-15, 2025
• A. Ochal, "On the dual nature of variational inequalities in quasi-static contact problem", Symposium on Recent Progress in Nonlinear Problems: Theory, Computation & Applications, Southwest Petroleum University Xindu District, Chengdu, China, June 13-15, 2025
• P. Bartman-Szwarc, "Modeling and Simulation of Dynamic Contact with Damped Normal Compliance", International Conference of China-Poland-Malasia on Differential Equations, Guangxi Minzu University, Nanning, China, June 9-12, 2025
• K. Bartosz, "Existence of weak solution for a dynamic Signorini's contact problem with nonmonotone friction law", International Conference of China-Poland-Malasia on Differential Equations, Guangxi Minzu University, Nanning, China, June 9-12, 2025
• A. Ochal, "A new penalty method for variational inequalities", International Conference of China-Poland-Malasia on Differential Equations, Guangxi Minzu University, Nanning, China, June 9-12, 2025
• P. Bartman-Szwarc, "Global Subgradient Method for Hemivariational Inequalities", Nonsmooth Problems with Applications in Mechanics, Olomouc, Czech Republic, May 19-23, 2025
• K. Bartosz, "Vanishing viscosity method for a noncoercive hyperbolic differential hemivariational inequality", Nonsmooth Problems with Applications in Mechanics, Olomouc, Czech Republic, May 19-23, 2025
• A. Ochal, "Penalty method in the study of nonsmooth quasistatic frictional contact with locking materials", Nonsmooth Problems with Applications in Mechanics, Olomouc, Czech Republic, May 19-23, 2025
• A. Ochal, "Dual approach to variational inequalities with applications", Workshop on Differential Equations and Their Applications, Będlewo, Poland, May 4 - 10, 2025
• S. Migórski, "Constrained quasi-variational-hemivariational inequalities with applications", The 14th AIMS Conference on Dynamical Systems and Differential Equations, Abu Dhabi, UAE, December 16 - 20, 2024
• A. Ochal, "A convergence criterion for elliptic quasivariational inequalities (SS96)” and “Time-dependent variational-hemivariational inequalities with applications (SS110)", The 14th AIMS Conference on Dynamical Systems and Differential Equations, Abu Dhabi, UAE, December 16 - 20, 2024
• A. Ochal, "Well-posedness results in the study of quasivariational inequalities", VIII Symposium on Nonlinear Analysis, Toruń, Poland, June 17-21, 2024
• K. Bartosz, "Existence of weak solution for a dynamic adhesive Signorini’s contact problem”, Dynamical Systems and Applications VI, DSA 2024, Łódź, Poland, June 26 - 28, 2024
• P. Bartman-Szwarc, "Aggregate Subgradient Method for Hemivariational Inequalities", Emerging trends in Applied Mathematics and Mechanics, A Coruña, Spain, May 20 - 24, 2024
• K. Bartosz, "Existence of weak solution for a dynamic Signorini’s contact problem with nonmonotone friction law”, Emerging trends in Applied Mathematics and Mechanics, A Coruña, Spain, May 20 - 24, 2024
• K. Bartosz, "Existence of weak solution for a dynamic Signorini’s contact problem with nonmonotone friction law”, Emerging trends in Applied Mathematics and Mechanics, A Coruña, Spain, May 20 - 24, 2024
• S. Migórski, "Quasi-Variational-Hemivariational Inequalities for Incompressible Navier - Stokes System with Bingham Fluid”, Emerging trends in Applied Mathematics and Mechanics, A Coruña, Spain (plenary talk), May 20 - 24, 2024
• A. Ochal, "On a new penalty method for quasivariational inequalities", Emerging trends in Applied Mathematics and Mechanics, A Coruña, Spain, May 20 - 24, 2024
• S. Migórski, "Variational inequality concepts in contact mechanics" Guangxi Mathematical Society Meeting, Liuzhou, P.R. China (invited talk), October 27-29, 2023
• P. Bartman-Szwarc, "Analysis of a convergence of a class of elliptic boundary hemivariational inequalities with application to steady-state heat transfer problems", Austral University, Rosario, Argentina (seminar), September 15, 2023
• A. Ochal, "A convergence criterium for penalty quasivariational inequalities", Austral University, Rosario, Argentina (seminar), September 15, 2023
• Bartman-Szwarc, P. "Numerical Methods for Variational Problems" Department of Mathematics, Austral University, Rosario, Argentina (seminar), September 13, 2023
• Prządka W., Bartman-Szwarc, P. "Numerical Methods for Variational Problems" Department of Mathematics, Austral University, Rosario, Argentina (seminar), September 13, 2023
• P. Bartman-Szwarc, "Numba accelerated scientific software engineering", Federation University in Ballarat, Australia (seminar), March 23, 2023
• Migórski, S. "Well-posedness of parabolic variational-hemivariational inequalites with unilateral constraints" The 10th International Congress on Industrial and Applied Mathematics, Waseda University, Tokyo, Japan (online talk), August 20-25, 2023
• Ochal, A. "Duality Arguments in the Analysis of a Viscoelastic Contact Problem" The 10th International Congress on Industrial and Applied Mathematics, Waseda University, Tokyo, Japan (online talk), August 20-25, 2023
• Bartosz, K. "Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem", VII International Conference on Computational Contact Mechanics, Turin, Italy (contributed talk) July, 5-7, 2023
• Bartosz, K. "Rothe Method for an adhesive contact of a nonlinear viscoelastic rod", Nonsmooth Problems with Applications in Mechanics, Będlewo, Poland (invited talk), June 17-22, 2023
• Migórski, S. "A Differential Quasi Variational-Hemivariational Inequalities: Well-Posedness and Application", Guangxi University for Nationalities, Nanning, China (online seminar), December 14, 2022
• Ochal, A. "Mathematical modeling of the world" Analysis in Tatra, Małe Ciche, Poland (off-site seminar), September 7-11, 2022
• Migórski, S. "On a class of variational inequalities" Analysis in Tatra, Małe Ciche, Poland (off-site seminar), September 7-11, 2022

Science Popularization Event

• S. Migorski delivered three invited presentations: "Solvability, Penalty, and Application of a System of Elliptic Quasi-Variational-Hemivariational Inequalities", "Concepts of Variational Inequalities and Applications" and "A Quasi-Variational-Hemivariational Inequality for Incompressible Navier-Stokes System with Bingham Fluid" at North Minzu University, Yinchuan, Ningxia Province, P.R. China, May 23-29, 2025 and on line on November 28, 2025.
• S. Migorski delivered an invited talk "Penalty Method for Elliptic and Parabolic Quasi Variational-Hemivariational Inequalities with Applications" at College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P.R. China, November 26, 2025.
• A. Ochal co-organized the "Analysis in Tatra 2025" seminar, Małe Ciche, September 16-20, 2025, promoting analysis in its broadest sense, including the one used in the project. The seminar-style nature of the international conference also facilitated the introduction of interdisciplinary topics to young mathematicians from the University of Warsaw and the Jagiellonian University. During this seminar, A. Ochal delivered a lecture to students, "Is optimization maximum benefit with minimum effort?".
• A. Ochal co-organized the mini-symposium "Recent trends in differential equations and inequalities" during Nonsmooth Problems with Applications in Mechanics, Olomouc, Czech Republic, May 19-23, 2025 and the mini-symposium "Variational and monotone methods with applications in mechanics" (MS07) during The 26th International Conference on Computer Methods in Mechanics, Lodz, Poland, July 8-11, 2025.
• S. Migorski delivered an invited talk "Penalty Methods for Variational and Hemivariational Inequalities with Application to Contact Mechanics", Sichuan University, Chengdu, P.R. China, June 27, 2025.
• S. Migorski delivered an invited lecture "Parabolic Stokes-Darcy Model" at School of Mathematical Sciences University of Electronic Science and Technology of China, Chengdu, P.R. China, June 26, 2025.
• S. Migorski delivered an invited talk "Nonsmooth Problems for Bingham Fluids" at Chengdu University of Technology, Chengdu, P.R. China, June 24, 2025.
• S. Migórski was a co-organizer and member of the scientific committee of The 3rd Conference on Recent Advances in Nonlinear Problems: Theory, Computation, and Applications, Southwest Petroleum University, Xindu District, Chengdu, China, June 13-15, 2025.
• S. Migorski delivered two invited talks: "A Version of a Novel Penalty Method for Quasi Variational-Hemivariational Inequality with Application" at Guangxi Minzu University, Nanning, and Yulin Normal University, Yulin, Guangxi, P.R. China, April 21 and June 6, 2025.
• S. Migorski delivered an invited presentation "Convergence of a Novel Penalty Method for Quasi Variational-Hemivariational Inequality with Application" at Guangxi University of Science and Technology, Liuzhou, Guangxi, P.R. China, May 30-June 5, 2025.
• S. Migórski was a member of scientific committee of the confenrence Emerging trends in Applied Mathematics and Mechanics, A Coruña, Spain, May 20 - 24, 2024 and a co-organizer of the special sesion "Evolution Equations with Applications to Control, Mathematical Modeling and Mechanics", during the 14th AIMS Conference on Dynamical Systems and Differential Equations, Abu Dhabi, UAE, December 16-20, 2024.
• A. Ochal was a member of scientific committee and organizing committee of the conference Dynamical Systems and Applications VI, Łódź, Poland, June 26-28, 2024, and a co-organizer of the mini-symposium „Recent trends in differential equations and inequalities” during the conference Emerging Trends in Applied Mathematics and Mechanics, A Coruña, Spain, May 20-24, 2024 and the mini-symposium "Differential Equations, Inequalities, and their Multifaceted Applications” during the conference Dynamical Systems and Applications VI, Łódź, Poland, June 26-28, 2024.
• A. Ochal was co-organizer of the off-site seminar "Analysis in Tatra," Małe Ciche (September 8-12, 2024) which promoted a broad understanding of analysis, including the kind used in the project. The seminar's interdisciplinary nature also facilitated the introduction of young mathematicians from the University of Warsaw (UW) and Jagiellonian University (UJ) to the topic. • S. Migórski was a member of program committee of the 2nd World Conference on Artificial Intelligence, Machine Learning and Data Science, Paris, France, October 19-20, 2023.
• A. Ochal was co-organizer of the off-site seminar "Analysis in Tatra," Małe Ciche, September 10-14, 2023.
• S. Migórski was co-organizer of minisymposium on "Recent Advances in Variational and Hemivariational Inequalities and Related Topics" during the 10th International Congress on Industrial and Applied Mathematics, Waseda University, Tokyo, Japan, August 20-25, 2023.
• S. Migórski was a member of organizing committee of the 6th International Conference on Mathematics and Statistics, (ICoMS 2023), Leipzig, Germany, July 14-16, 2023.
• S. Migórski, A. Ochal and K. Bartosz were co-organizers of the conference Nonsmooth Problems with Applications in Mechanics, Będlewo, Poland, June 17-22, 2023.
• S. Migórski was co-organizer of special sesion "Optimal Control of Finite and Infinite Dimensional Dynamic Systems and their Applications" during the 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Wilmington, NC USA, May 31-June 4, 2023.
• A. Ochal and K. Bartosz were co-organizers of the off-site seminar "Analysis in Tatra," Małe Ciche, September 7-11, 2022.

Other forms of disseminating results

• As part of the team's activities, a weekly scientific seminar is held to discuss the project results.
• A Short Course on "Optimization Theory and Variational Inequalities”, at School of Sciences and Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu, P.R. China, April-May 2025. Within the framework of international cooperation in the project, S. Migorski is a supervisor of a post-doc researcher prof. Yaojia Zhang from Southwest Petroleum University, Chengdu. On June 30, 2025, Prof. Zhang was awarded the Chinese Government Scholarship to sponsor his visit for one academic year 2025-2026 at the Jagiellonian University.
• A. Ochal was the guest editor for special issue of Discrete and Continuous Dynamical Systems - Series B (DCDS-B) Vol. 30, No. 11 (2025).
• A. Ochal has been a member of the Section of Applications of Mathematics in Mechanics - Committee of Mechanics of the Polish Academy of Sciences.

Web page

• The project website https://opus.kos.ii.uj.edu.pl/Home.html, containing the main information and results of the project, is a subpage of the website of the Chair of Optimization and Control of the Faculty of Mathematics and Computer Science of the Jagiellonian University.

Inclusion in a Public Database

For computer simulations, used e.g. in publication 33 and conference publication 1, the CONMECH software was created and developed and is available on the GitHub.