Here we give short overview of the research activites of the Division of Mathematical Modelling. If you are interested in the research done by the other institutions participating on the study programme mathematical modelling, please see their own webpages. (Department of Mathematical Analysis, Department of Numerical Mathematics, Department of Surface and Plasma Science, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University and the Institute of Mathematics and Institute of Computer Science of the Academy of Sciences of the Czech Republic to name a few.)
In brief our research fields are the following:
- continuum mechanics and thermodynamics,
- mathematical analysis of partial differential equations,
- numerical analysis and computer simulations.
Research projects that were/are solved by our group are listed below. Recently, our main research project was the ERC-CZ project Implicitly constituted material models: from theory through model reduction to efficient numerical methods
Our group is internationally well recognized and we present outcomes of our research at major international events. Recently, we organized, among others, a mini-symposium at the 6th European Congress of Mathematics, a mini-symposium at the SIAM Annual Meeting 2013, and a workshop in the Banff International Research Station for Mathematical Innovation and Discovery. We regularly organize international schools on advanced mathematical methods in theory of partial differential equations.
We have been active in forming two larger research platforms, namely University Center for Mathematical Modeling, Applied Analysis and Computational Mathematics (MathMAC) and the Nečas Center for Mathematical Modeling.
For a list of publications see the corresponding web page.
Members of the Division of Mathematical Modelling are principal investigators and team members in various research projects. See below for a list of projects that have been solved since 2013. (We list only projects that we lead as principal investigators.)
Ministry of Education, Youth and Sports, Czech Republic
- 2012–2017, ERC-CZ, Implicitly constituted material models: from theory through model reduction to efficient numerical methods, principal investigator Josef Málek
Czech Science Foundation
The members of the Division of Mathematical Modelling have successfully applied for many Czech Science Foundation grants. It is worth to note that the grants come from various panels (101 – Mechanical Engineering, 107 – Materials and Metallurgy, 201 – Mathematics).
- 2020–2024, GA ČR GX20-11027X , Mathematical analysis of partial differential equations describing far-from-equilibrium open systems in continuum thermodynamics, principal investigator Miroslav Bulíček
- 2018–2020, GA ČR 18-12719S Thermodynamical and mathematical analysis of flows of complex fluids, principal investigator Josef Málek
- 2017–2019, GA ČR 17-15498Y Multiscale nonequilibrium thermodynamics, principal investigator Michal Pavelka
- 2017–2019, GA ČR 17-04301S Advanced mathematical methods for dissipative evolution equations, principal investigator Martin Kružík
- 2015–2017, GA ČR GJ15-14263Y, Generation of meltwater and transport processes in the ice shell of Europa, principal investigator Ondřej Souček
- 2012–2016, GA ČR 107/12/0121, A mechanism of ultra-fine substructure formation induced by severe plastic deformation, principal investigator Jan Kratochvíl
- 2012–2014, GA ČR 101/12/P074, Behaviour of incompressible fluid-like materials with pressure dependent material moduli, principal investigator Vít Průša
- 2010–2014, GA ČR 201/10/0357, Modern mathematical and computational models for inelastic processes in solids, principal investigator Tomáš Roubíček
- 2009–2013, GA ČR 201/09/0917, Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials, principal investigator Josef Málek
- 2013–2014, Nadační fond Karla Janečka, Kvalitativní analýza nestlačitelných Navierových-Stokesových-Fourierových rovnic, principal investigator Miroslav Bulíček
- 2012–2017, Charles University, Univerzitní centrum matematického modelování, aplikované analýzy a výpočtové matematiky, principal investigator Josef Málek
- 2018–2023, Charles University, Univerzitní centrum matematického modelování, aplikované analýzy a výpočtové matematiky, principal investigator Josef Málek
The members of the Division of Mathematical Modelling organize or participate in organization of many scientific meetings and schools focused on various subjects.
The school with longest tradition is the school Mathematical theory in fluid mechanics that is organized biannually since 1997, and that has been recently split to two schools organised under the auspices of the
European Mathematical Society. The two successor schools are schools Mathematical Modelling, Numerical Analysis and Scientific Computing and Mathematical Aspects of Fluid Flows.