Oct 25, 2011 
SFB 647 
Nov 01, 2011 
Andrey Muravnik (Peoples' Friendship University Moscow) 
The Cauchy problem for parabolic differentialdifference equations:
integral representations of solutions and their longtime behavior 
Parabolic equations (including singular ones) containing
translation (generalized translation) operators
acting with respect to spatial variables are considered. Integral
representations of their classical solutions are found and
asymptotic closeness (stabilization) theorems are proved for their solutions.
It turns out that there are principally new effects of the longtime
behavior of the above solutions caused by the nonlocal nature of the equation.
Moreover, those effects hold even in the case
where only loworder terms of the equation are nonlocal.

Nov 08, 2011 
SFB 647 
Nov 22, 2011 
Carlo Laing (Massey University New Zealand) 
Fronts and bumps in spatially extended Kuramoto networks 
We consider moving fronts and stationary “bumps” in networks of nonlocally coupled phase oscillators.
Fronts connect regions of high local synchrony with regions of complete asynchrony,
while bumps consist of spatiallylocalised regions of partiallysynchronous oscillators surrounded by complete asynchrony.
Using the OttAntonsen ansatz we derive nonlocal differential equations which describe the network dynamics in the continuum limit.
Front and bump solutions of these equations are studied by either “freezing” them
in a travelling coordinate frame or analysing them as homoclinic or heteroclinic orbits.
Numerical continuation is used to determine parameter regions in which such solutions exist and are stable.

Nov 29, 2011 
SFB 647 
Dec 06, 2011 
Svetlana Gurevich (Westfälische WilhelmsUniversität Münster) 
Destabilization of localized structures induced by delayed feedback 
Dec 13, 2011 
Thomas Wagenknecht (University of Leeds) 
Homoclinic snaking: different ways to kill the snakes 
SFB 647 
Jan 10, 2012 
SFB 647 
Jan 24, 2012 
Eugen Zhang (Oregon State University) 
Efficient Morse Decomposition of Vector Fields 
Traditional vector field topology relies on the ability to accurately compute trajectories, which is difficult to achieve due to noise and error. Morse decomposition addresses this issue. However, computing Morse decomposition given a simulation data set can be challenging due to the complexity in both the flows and the underlying domains. In this talk I will discuss how to effectively compute Morse decomposition in a hierarchical fashion. The results have been applied to a number of simulation data sets.

Jan 31, 2012 
SFB 647 
Feb 06, 2012 Monday 16:15 Free University 
Daria Apushkinskaya (Saarland University) 
TwoPhase Parabolic Obstacle Problems: L^{∞}estimates for Derivatives of Solutions 
Consider the twophase parabolic obstacle problem with nontrivial Dirichlet condition
Δu − ∂_{t}u 
= 
λ^{+}χ_{{u>0}}
− λ^{−}χ_{{u<0}}

in Q=Ω×(0;T), 
u 
= 
φ 
on ∂_{p}Q. 
Here T<+∞, Ω ⊂ R^{n} is a given domain, ∂_{p}Q denotes the parabolic boundary of Q, and λ^{±} are nonnegative constants satisfying λ^{+}+λ^{−}>0. The problem arises as limiting case in the model of temperature control through the interior.
In this talk we discuss the L^{∞}estimates for the secondorder space derivatives D^{2}u near the parabolic boundary ∂_{p}Q. Observe that the case of general Dirichlet data cannot be reduced to zero ones due to nonlinearity and discontinuity at u=0 of the righthand side of the first equation.
The talk is based on works in collaboration with Nina Uraltseva.

Free University,
Institute of Mathematics, 14195 Berlin,
Arnimallee 3 (rear building), room 130 
Feb 07, 2012 17:15 Free University 
Nina Uraltseva (St.Petersburg State University) 
TwoPhase Parabolic Obstacle Problem:
Regularity Properties of the Free Boundary 
In this talk we describe the methods, developed in the last decade, for studying the regularity of the free boundary in the vicinity of branch points. These methods are based on the use of various monotonicity formulas, blowup technique and some observations of geometric nature. 
Free University,
Institute of Mathematics, 14195 Berlin,
Arnimallee 6, room 031 
Feb 14, 2012 
NN 
tba 