| 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 |
|
Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !
Last change: Jan. 23, 2013
