The minisymposium on "Higher-order evolution equations" will be organized within the European Congress of Mathematics which was planned to take place in Portorož, Slovenia, from June 20 - 26, 2021, but will be held completely online in that period. If you wish to attend the minisymposium please follow the instructions for registration and abstract submission.

Description

Nonlinear evolution equations of order four and six in spatial derivatives arise in various contexts of mathematical physics. The most prominent examples are the Cahn-Hillard equation describing spinodal decomposition, followed by the fourth-order thin-film equations describing dynamics of the thickness of thin viscous fluid films. Other examples include fourth-order equations in semiconductor modelling, statistical description of interface fluctuations in spin systems, Bose-Einstein condensates, image processing etc, while sixth-order thin-film equations appear as reduced models in fluid-structure interaction problems. 

The understanding of the dynamics of higher-order evolution equations, possibly extended by stable or unstable lower-order terms, is of high relevance in industrial applications, for instance in an emerging area of so-called lab-on-a-chip technologies. This minisymposium will bring together renowned experts in the area of mathematical physics, partial differential equations and numerical analysis with aim of stipulating the interplay between the three main aspects of higher-order equations: modelling, analysis and numerics. 

Key challenges like positivity, stability of solutions, speed of propagation, construction of structure preserving numerical schemes and justification of higher-order equations as approximate models will be explored.

Confirmed speakers

• Bertram Düring (Uni Warwick) - A Lagrangian scheme for the solution of nonlinear diffusion equations
• Manuel Gnann (TU Delft) - Weak solutions to the stochastic thin-film equation with nonlinear noise in divergence form
• Marco Fontelos (ICMAT Madrid) - Discretely selfsimilar solutions for fourth order PDEs in lubrication models
• Daniel Matthes (TU München) - Gradient flow structure of a sixth order parabolic equation
• Demetrios Papageorgiou (Imperial C. London) - High order PDEs arising in immiscible multilayer flows
• Carola-Bibiane Schönlieb (Uni Cambridge) - Higher-Order Total Directional Variation
• Mario Bukal (Uni Zagreb) - Sixth-order thin-film equations as reduced models for fluid-structure interaction problems

Organizer

Mario Bukal (Uni Zagreb)