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# Abstracts

**KEYNOTE SPEAKERS**

**Andreas Münch (U Oxford), Wednesday**

*Fingering Instabilities in Thin Film Dynamics.*

**Dorothee Knees (WIAS Berlin), Thursday**

*Weak solutions for rate-independent systems illustrated at an example for crack propagation.*

In the corresponding models it is assumed that the actual state of the material can be completely characterized by the displacement field and a collection of internal variables that characterize for instance the damage state or the plastic deformation. The model describing the evolution of these quantities with respect to external loadings consist of a (quasistatic) balance of forces resulting in a system of linear elliptic equations that is coupled with an evolutionary variational inequality describing the changes of the internal variables. This coupled system can be derived from an energy functional and a dissipation potential, which, due to rate-independence, is positively homogeneous of degree one.

Since in many applications the energy functional is not simultaneously convex with respect to the displacements and the internal variables, solutions of the evolution system might be discontinuous in time. Hence, weak formulations and suitable jump criteria are needed that lead to physically reasonable solutions.

In this lecture we discuss different possibilities to define weak solutions and illustrate the predictions with a model describing the propagation of a single crack in a brittle elastic material.

**Martin Burger (Münster U), Friday**

*Mathematics of Collective Behaviour - Complex Patterns and Minimal Models.*

This talk will provide an overview of the modelling from a mathematician's viewpoint and demonstrate that (besides pre-existing patterns in the environment) the main source of pattern formation is an interaction of two effects, namely long-range attraction and short-range repulsion. In macroscopic models based on partial differential equations, this typically means a combination of a (nonlinear) diffusion term with an integral operator.

In order to understand this interplay minimal mathematical models will be derived and analyzed, which contribute strongly to the understanding of basic mechanisms of pattern formation and phase transitions with respect to system parameters as found in real data and detailed microscopic simulations.

**INVITED TALKS**

**Tobias Ahnert (TU Berlin)**

*Multiphase model for dilute and non-dilute flow of suspensions.*

**Marion Dziwnik (TU Berlin)**

*Stability analysis with non-constant base states*

**Matt Hennessy (University of Oxford)**

*Bilayer formation and topological transitions in a diffusive phasefield model*

**Sebastian Jachalski (WIAS Berlin)**

*Structure formation in thin liquid bilayers*

**Georgy Kitavtsev (MPI Leipzig)**

*Coarsening Rates for the Dynamics of Interacting Slipping Droplets*

**Alexander Linke (WIAS Berlin)**

*On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime*

**Marco Morandotti (Inst. Sup. Tec., Lisbon)**

*Dynamics for a system of screw dislocations*

**Michael Köpf (École Normale Supérieure, Paris, France)**

*A continuum model of wound healing in epithelial tissues*

**Dirk Peschka (WIAS Berlin)**

*Treatment of triple junctions in thin-film models*

**Filip Rindler (U Warwick)**

*Orientation-preserving Young measures*

**Hao Wu (Fudan U)**

*Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flow*

**CONTRIBUTED TALKS**

**Vladimir Bobkov (Ufa Science Center, RAS)**

*On the behaviour of branch of gound state solutions to the system of elliptic equations*

**Karoline Disser (WIAS Berlin)**

*On gradient structures for Markov chains and the passage to Wasserstein gradient flows*

**Svetlana Gurevich (Münster U)**

*Delayed feedback control of localized structures in reaction-diffusion systems*

**Patrick van Meurs (Eindhoven U Tech.)**

*Collective Behaviour of Walls of Dislocations*

**Elias Pipping (FU Berlin)**

*Variational methods for rate- and state-dependent friction problems.*

**Sina Reichelt (WIAS Berlin)**

*Two-scale homogenization in nonlinear reaction-diffusion systems with small diffusion*

**Fabian Spill (Oxford U)**

*Modelling of Angiogenesis*

**Giles Shaw (Cambridge U)**

*Continuous Extension of Integral Functionals over W^{1,1}.*

**Miguel Yangari (U Toulouse)**

*Fast propagation for fractional kpp equations with slowly decaying initial conditions.*

**Markus Wilczek (Münster U)**

*Synchronization effects in Cahn-Hilliard models for Langmuir-Blodgett transfer*

**Martijn Zaal (Bonn U)**

*Variational modeling of osmotic cell swelling*