EXPRO 2020 Analysis of partial differential equations


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 team member (2021) dynamical systems, spectral stability davis@karlin.mff.cuni.cz
Mark Dostalík PhD student (2020--2021, PhD thesis defended in October 2021) continuum thermodynamics dostalik@karlin.mff.cuni.cz
Michael Zelina PhD student partial differential equations zelina.michael@gmail.com
Michal Bathory PhD student (2020, PhD thesis defended in September 2020) partial differential equations, viscoelastic fluids bathory@karlin.mff.cuni.cz
Tomáš Los PhD student (2021--) partial differential equations tomas.los@mff.cuni.cz
Buddhika Priyasad Postdoc (2022--) partial differential equations buddhikapriyasad@gmail.com
Victoria Patel Postdoc (2022--) partial differential equations victoria.patel@maths.ox.ac.uk

© 2019–2022 Miroslav Bulíček; Last modified: Fri 04 Feb 2022 09:54:30 AM CET; Powered by w3.css