Project Mathematical analysis of partial differential equations describing far-from-equilibrium open systems in continuum thermodynamics is a fundamental research project funded by the Czech Science Foundation, grant number 20-11027X, in the framework of EXPRO programme. The principal investigator is Miroslav Bulíček (Charles University) and the duration of the project is 2020--2024.
Most of the processes that are of interest in continuum thermodynamics take place far from equilibrium. These processes frequently give birth to dissipative structures that dominate the dynamical behaviour. The existing mathematical approaches applicable for the description of the dissipative structures however face principal difficulties. Either the physically relevant description is achieved at the price of sacrificing the mathematical rigour, or the existing approaches are fully rigorous, but they are of no physical relevance. Our aim is to overcome this gap. For the physically relevant models we will develop constructive methods for the description of the structures in terms of lower dimensional subsystems. Obstacles such as the lack of regularity of the solution operators will be dealt with the method of trajectories. The project is expected to open entirely new perspectives in the theory of dynamical systems and to considerably expand the understanding of complex behaviour of dynamical systems in continuum thermodynamics.
Keywords: nonlinear partial differential equations, continuum themodynamics, dynamical systems
| Name | Position | Expertise | Contact |
|---|---|---|---|
| Miroslav Bulíček | principal investigator | partial differential equations, continuum thermodynamics | mbul8060@karlin.mff.cuni.cz |
| Tomáš Bárta | team member | integrodifferential equations | barta@karlin.mff.cuni.cz |
| Dalibor Pražák | team member | dynamical systems | prazak@karlin.mff.cuni.cz |
| Vít Průša | team member | continuum thermodynamics | prusv@karlin.mff.cuni.cz |
| Petr Kaplický | team member | partial differential equations, regularity | kaplicky@karlin.mff.cuni.cz |
| Josef Málek | team member | partial differential equations, continuum thermodynamics | malek@karlin.mff.cuni.cz |
| Paige Davis | postdoc (2021) | dynamical systems, spectral stability | pgn.davis@gmail.com |
| Pablo Alexei Gazca Orozco | postdoc (2021) | dynamical systems, spectral stability | gazca@karlin.mff.cuni.cz |
| Daniel Lear Claveras | postdoc (2021) | partial differential equations | daniel.lear@unican.es |
| Tomáš Los | postdoc (2023) | partial differential equations | tomas.los@mff.cuni.cz |
| Buddhika Priyasad | postdoc (2022--2023) | partial differential equations | buddhikapriyasad@gmail.com |
| Michal Bathory | PhD student (2020, PhD thesis defended in September 2020) | partial differential equations, viscoelastic fluids | |
| Mark Dostalík | PhD student (2020--2021, PhD thesis defended in October 2021) | continuum thermodynamics | |
| Tomáš Los | PhD student (2021--2022, PhD thesis defended in September 2022) | partial differential equations | |
| Stanislav Mosný | master student (2022--2023), master thesis defended in June 2023 | partial differential equations | |
| Emil Skříšovský | PhD student (2020) | partial differential equations | |
| Ladislav Trnka | master student (2024), master thesis defended in June 2025 | numerical methods, partial differential equations | |
| Ondřej Váša | master student (2022--2023), master thesis defended in September 2023 | partial differential equations | |
| Martin Vejvoda | PhD student (2024) | mathematical modelling | |
| Lucie Wintrová | master student (2023--2024, master thesis defended in June 2024) | partial differential equations | |
| Michael Zelina | PhD student (2021--2024), PhD thesis defended in September 2025 | partial differential equations |
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