EXPRO 2020 Analysis of partial differential equations

ABOUT

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.

Abstract

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

Team

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
Michal Bathory PhD student partial differential equations, viscoelastic fluids bathory@karlin.mff.cuni.cz
Mark Dostalík PhD student continuum thermodynamics dostalik@karlin.mff.cuni.cz

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