Weakly coupled systems of conservation laws on moving surfaces
Tuesday, 2.5.17, 15:00-16:00, Raum 226, Hermann-Herder-Str. 10
Dissertationsthema
Tuesday, 23.5.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The Half-Wave Maps Equation
Tuesday, 20.6.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The half-wave maps equation (HWM) is a newly found geometric evolution equation, which arises as a universal continuum limit for the dynamics of completely integrable spin systems with long-range interactions (also known as Haldane-Shastry and Calogero-Moser models). After a brief summary on the physical background, I will highlight some intriguing mathematical features of (HWM). In particular, I will discuss a complete and explicit classification of its traveling solitary waves and the spectral analysis of the corresponding linearized operator. Finally, I will comment on the close relations and striking differences of (HWM) with the Schrödinger maps equation (Landau-Lisfhitz equation in ferromagnetism) and the wave maps equation (nonlinear sigma model in anti-ferromagnetism).\n
Keller-Segel models coupled to fluid equations.
Tuesday, 20.6.17, 15:15-16:15, Raum 226, Hermann-Herder-Str. 10
We consider chemotaxis equations coupled to the Navier-Stokes equations, which is a mathematical model describing the dynamics of oxygen, swimming bacteria (Bacillus subtilis), and viscous incompressible fluids. It is not known for this model in two and three dimensions whether or not regular solutions exist globally in time or develop a singularity in a finite time, in case that initial data are sufficiently smooth. We discuss existence of regular solutions under a certain type of conditions and asymptotics as well as temporal decays of solutions, as time tends to infinity.
Globale Existenz schwacher Lösungen für die Interaktion eines Newtonschen Fluides mit einer linearen, transversalen Koiter-Schale unter natürlichen Randbedingungen
Tuesday, 4.7.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Bio-inspired materials research: Tapping the wondrous world of plant structures and functions
Thursday, 6.7.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Depinning as a coagulation process
Tuesday, 25.7.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Phase-Field Models for Thin Elastic Structures
Tuesday, 25.7.17, 16:45-17:45, Raum 226, Hermann-Herder-Str. 10
We will discuss phase-field approximations of a\ngeometric energy functional defined on surfaces embedded\ninto a small container. The novelty in our work is the\ncontrol of the connectedness of limiting surfaces by a\npenalty on the diffuse interface level. This is achieved by\npenalising a double integral of a suitable geodesic\ndistance function. We will also show that no finer\ntopological control can be achieved and present numerical\nevidence of the effectiveness of our method.\n