Workshop 2020 Partial differential equations

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 ( 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.


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


Name Institution Country Lecture
Benjamin AmbrosioUniversity of Le HavreFranceBifurcations, pattern formation and synchronization in a few RD systems and networks of RD systems
Tomáš BártaCharles UniversityCzech RepublicAsymptotic behaviour of solutions to abstract wave equations with damping
Miroslav BulíčekCharles UniversityCzech RepublicPartial differential equations describing far-from-equilibrium open systems
Dieter BotheTU DarmstadtGermanyOn the structure of continuum thermodynamical diffusion fluxes
Jose CarrilloUniversity of OxfordUnited KingdomNonlinear Aggregation-Diffusion Equations: Gradient Flows, Free Energies and Phase Transitions
Michele Coti-ZelatiImperial College LondonUnited KingdomStationary Euler flows near Kolmogorov and Poiseuille
Marie DoumicSorbonne UniversitéFranceTransient oscillatory behaviours for polymerisation-depolymerisation systems of Becker-Döring type
Patrick FarrellUniversity of OxfordUnited KingdomComputing disconnected bifurcation diagrams of partial differential equations
Eduard FeireislCzech Academy of SciencesCzech RepublicNavier-Stokes-Fourier system with general in/out flow boundary conditions
Mariana HaragusUniversité de Franche-ComtéFranceBifurcation of symmetric domain walls for the Bénard-Rayleigh convection problem
Claire Chainais-HillairetUniversité Lille 1 Sciences et TechnologiesFranceLarge-time behavior of solutions to finite volume discretizations
Ansgar JüngelVienna University of TechnologyAustriaAnalysis of cross-diffusion systems with entropy structure
Petr KaplickýCharles UniversityCzech RepublicUniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth
Rich KerswellUniversity of CambridgeUnited KingdomNonlinear non-modal stability analysis: how to escape a basin of attraction efficiently
Jean-Philippe LessardMcGill UniversityCanadaSpontaneous periodic orbits in the Navier-Stokes flow
Josef MálekCharles UniversityCzech RepublicOn nonlinear problems of parabolic type with implicit constitutive equations involving flux
Clément MouhotUniversity of CambridgeUnited KingdomUnified approach to fluid approximation of linear kinetic equations with heavy tails
Ayman MoussaSorbonne UniversitéFranceConcentration (or not) in the Vlasov-Navier-Stokes system
Milan PokornýCharles UniversityCzech RepublicWeak solutions for a version of compressible Oldroyd-B model without stress diffusion
Dalibor PražákCharles UniversityCzech RepublicFinite-dimensional reduction of dissipative dynamical systems
Vít PrůšaCharles UniversityCzech RepublicThermodynamics of viscoelastic rate-type fluids and its implications for stability analysis
Alexander RammKansas State UniversityUnited StatesDynamical systems method (DSM) for solving operator equations
James RobinsonUniversity of WarwickUnited KingdomApproximating the Navier-Stokes equations on R^3 with large periodic domains
Alastair M. RucklidgeUniversity of LeedsUnited KingdomSpatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems
Francesco SalvaraniUniversita di PaviaItalyTwo-scale homogenization of the linear Boltzmann equation in energy
Endre SuliUniversity of OxfordUnited KingdomMcKean--Vlasov diffusion and the well-posedness of the Hookean bead-spring chain model for dilute polymeric fluids
Athanasios TzavarasKing Abdullah University of Science and TechnologySaudi ArabiaThe system of polyconvex thermoelasticity and its approximation via variational schemes

Last update: 8th September 2020

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