Nonlinear Dynamics at the Free University Berlin

Winter 2012/2013

Oberseminar Nonlinear Dynamics



Oct 16, 2012 Igor Franovic
(currently University Potsdam)
Excitable systems under noise and delayed couplings: Self-organization and paradigm for hierarchies of mean-field approximations
Oct 30, 2012 Kristial Uldall Kristiansen
(Technical University of Denmark)
On slow manifolds where the fast normal motion is oscillatory
Nov 6, 2012 SFB 647
Nov 13, 2012 Vasily Denisov
(Lomonosov Moscow State University)
On stabilization problem for parabolic equations
We discuss necessary and sufficient conditions on the lower order coefficients of parabolic equations under which the solution of the Cauchy problem stabilizes (x-uniformly) to zero on every compact in Euclidean space. Bounded and growing initial functions are considered.
Nov 19-21, 2012 Workshop on coupled networks, patterns and complexity
Nov 27, 2012 Klaus Böhmer
(Philipps-Universität Marburg)
Dew drops on spider webs: a symmetry breaking bifurcation for a parabolic differential-algebraic equation
Lines of dew drops on spider webs are frequently observed on cold mornings. In this lecture we present a model explaining their generation. Although dew is supposed to condense somehow evenly along the thread, only lines of drops are observed along the spider thread. What are the reasons for this difference? We try to give an explanation by concentrating on some essential aspects only. This every-day observation is an example of one of the fascinating scenarios of nonlinear problems, symmetry breaking bifurcation. Despite many simplifications the model still provides very interesting mathematical challenges. In fact the necessary mathematical model and the corresponding numerical methods for this problem are so complicated that in its full complexity it never has been studied before. We analyse and numerically study symmetry breaking bifurcations for a free boundary value problem of a degenerate parabolic differential-algebraic equation employing a combination of analytical and numerical tools.
Dec 4, 2012 SFB 647
Dec 11, 2012 Sergio Oliva
(University Sao Paulo, Brasil)
Inflammatory phase dynamics in diabetic wounds: a PDE approach
The objective of the present paper is the modeling and analysis of the dynamics of macrophages and certain growth factors in the inflammatory phase, the first one of the wound healing process. It is the phase where there exists a major difference between diabetic and nondiabetic wound healing, an effect that we will consider in this talk.
We will propose and analyze a partial differential equation as a model for the interaction of some of the crucial elements involved in this phase of the wound healing. This model will generalize a previous existing ODE model.The final model is a system of 3 PDE equations with nonlinear boundary conditions and we show that it is a well posed problem both from a mathematical and biological point of view. More concretely, we will prove there exists a bounded invariant set where all the solutions are global and positive, and show some numerical experiments.
Work done in collaboration with Neus Consul and Marta Pellicer.
Jan 8, 2013 SFB 647
Jan 15, 2013 Shalva Amiranashvili
(WIAS Berlin)
Extreme events in optical supercontinuum
Optical supercontinuum is a conversion of a short light pulse into a complicated filed pattern with an ultra-wide spectrum. Many interesting objects are hiding behind this pattern, including solitons, linear wave packets, and short-living sub-pulses with the extremely high intensities. Detailed insight into the supercontinuum is provided by a numerical solution of the corresponding propagation equation.
Jan 29, 2013 Frits Veerman
(Leiden University)
Pulses in singularly perturbed reaction-diffusion systems
The existence of pulse solutions in a two component system of singularly perturbed reaction-diffusion equations is established using geometric singular perturbation theory. The stability of these pulse solutions can be analysed using Evans functions techniques, leading to explicit expressions, even in the general setting. A Gierer-Meinhardt system with an additional slow nonlinear term is used as an explicit example, showing new phenomena.
Feb 5, 2013 SFB 647
Feb 12, 2013 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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