The workshop is an online and upscaled replacement event for minisymposium Partial differential equations describing far-from-equilibrium open systems that was expected to be a part of the cancelled 8th European Congress of Mathematics (https://www.8ecm.si/). The workshop will take place online in the week 21st -- 24th September 2020 at 14:00 -- 18:00 Prague time. The workshop is organised within the framework of project EXPRO 2020: Mathematical analysis of partial differential equations describing far-from-equilibrium open systems in continuum thermodynamics, and it is not an official event linked to the cancelled 8th European Congress of Mathematics.

Abstract

Modern continuum thermodynamics provides a framework for mathematical modelling of behaviour of fluids, gases and solids at time and length scales accessible to direct human experience. It is indispensable in modelling of various important natural phenomena and also phenomena met in engineering practice. Most of the processes that are of interest in this field are, in the language of thermodynamics, strongly non-equilibrium processes or entropy producing processes. Concerning the mathematical point of view, one needs to deal with complicated dynamics of infinite dimensional dynamical systems.

The far-from-equilibrium processes give birth to dissipative structures (known also as self-sustaining processes, coherent structures or convectons) which can be understood as large scale structures that dominate the behaviour of the system. Such structures have been identified in many experiments and to some extent in simulations based on numerical solution of the corresponding system of partial differential equations. A solid mathematical theory that would allow one to study the dissipative structures is however largely non-existing. The aim of the symposia is to present a variety of available new tools and methods that could help one to understand far-from-equilibrium processes from the rigorous mathematical point of view.

Keywords: nonlinear partial differential equations, continuum themodynamics, dynamical systems

Lectures

Name	Institution	Country	Lecture
Benjamin Ambrosio	University of Le Havre	France	Bifurcations, pattern formation and synchronization in a few RD systems and networks of RD systems
Tomáš Bárta	Charles University	Czech Republic	Asymptotic behaviour of solutions to abstract wave equations with damping
Miroslav Bulíček	Charles University	Czech Republic	Partial differential equations describing far-from-equilibrium open systems
Dieter Bothe	TU Darmstadt	Germany	On the structure of continuum thermodynamical diffusion fluxes
Jose Carrillo	University of Oxford	United Kingdom	Nonlinear Aggregation-Diffusion Equations: Gradient Flows, Free Energies and Phase Transitions
Michele Coti-Zelati	Imperial College London	United Kingdom	Stationary Euler flows near Kolmogorov and Poiseuille
Marie Doumic	Sorbonne Université	France	Transient oscillatory behaviours for polymerisation-depolymerisation systems of Becker-Döring type
Patrick Farrell	University of Oxford	United Kingdom	Computing disconnected bifurcation diagrams of partial differential equations
Eduard Feireisl	Czech Academy of Sciences	Czech Republic	Navier-Stokes-Fourier system with general in/out flow boundary conditions
Mariana Haragus	Université de Franche-Comté	France	Bifurcation of symmetric domain walls for the Bénard-Rayleigh convection problem
Claire Chainais-Hillairet	Université Lille 1 Sciences et Technologies	France	Large-time behavior of solutions to finite volume discretizations
Ansgar Jüngel	Vienna University of Technology	Austria	Analysis of cross-diffusion systems with entropy structure
Petr Kaplický	Charles University	Czech Republic	Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth
Rich Kerswell	University of Cambridge	United Kingdom	Nonlinear non-modal stability analysis: how to escape a basin of attraction efficiently
Jean-Philippe Lessard	McGill University	Canada	Spontaneous periodic orbits in the Navier-Stokes flow
Josef Málek	Charles University	Czech Republic	On nonlinear problems of parabolic type with implicit constitutive equations involving flux
Clément Mouhot	University of Cambridge	United Kingdom	Unified approach to fluid approximation of linear kinetic equations with heavy tails
Ayman Moussa	Sorbonne Université	France	Concentration (or not) in the Vlasov-Navier-Stokes system
Milan Pokorný	Charles University	Czech Republic	Weak solutions for a version of compressible Oldroyd-B model without stress diffusion
Dalibor Pražák	Charles University	Czech Republic	Finite-dimensional reduction of dissipative dynamical systems
Vít Průša	Charles University	Czech Republic	Thermodynamics of viscoelastic rate-type fluids and its implications for stability analysis
Alexander Ramm	Kansas State University	United States	Dynamical systems method (DSM) for solving operator equations
James Robinson	University of Warwick	United Kingdom	Approximating the Navier-Stokes equations on R^3 with large periodic domains
Alastair M. Rucklidge	University of Leeds	United Kingdom	Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems
Francesco Salvarani	Universita di Pavia	Italy	Two-scale homogenization of the linear Boltzmann equation in energy
Endre Suli	University of Oxford	United Kingdom	McKean--Vlasov diffusion and the well-posedness of the Hookean bead-spring chain model for dilute polymeric fluids
Athanasios Tzavaras	King Abdullah University of Science and Technology	Saudi Arabia	The system of polyconvex thermoelasticity and its approximation via variational schemes

Last update: 8th September 2020