Nonlinear Dynamics at the Free University Berlin

Winter 2011/12

Oberseminar Nonlinear Dynamics



Oct 25, 2011 SFB 647
Nov 01, 2011 Andrey Muravnik
(Peoples' Friendship University Moscow)
The Cauchy problem for parabolic differential-difference equations: integral representations of solutions and their long-time 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 long-time behavior of the above solutions caused by the non-local nature of the equation. Moreover, those effects hold even in the case where only low-order terms of the equation are non-local.
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 non-locally coupled phase oscillators. Fronts connect regions of high local synchrony with regions of complete asynchrony, while bumps consist of spatially-localised regions of partially-synchronous oscillators surrounded by complete asynchrony. Using the Ott-Antonsen ansatz we derive non-local 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 Wilhelms-Universität 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
Free University
Daria Apushkinskaya
(Saarland University)
Two-Phase Parabolic Obstacle Problems: L-estimates for Derivatives of Solutions
Consider the two-phase parabolic obstacle problem with non-trivial Dirichlet condition
Δu − ∂tu = λ+χ{u>0} − λχ{u<0} in Q=Ω×(0;T),
u = φ on ∂pQ.
Here T<+∞, Ω ⊂ Rn is a given domain, pQ denotes the parabolic boundary of Q, and λ± are non-negative constants satisfying 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 second-order space derivatives D2u near the parabolic boundary pQ. Observe that the case of general Dirichlet data cannot be reduced to zero ones due to non-linearity and discontinuity at u=0 of the right-hand 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
Free University
Nina Uraltseva
(St.Petersburg State University)
Two-Phase 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, blow-up technique and some observations of geometric nature.
Free University, Institute of Mathematics, 14195 Berlin, Arnimallee 6, room 031
Feb 14, 2012 NN tba

Time and Place

Talks usually take place on Tuesday at 3:15 p.m.
at the Weierstraß Institute
Ehrhard-Schmid-Hörsaal, Mohrenstr. 39, 10117 Berlin.

Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !


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