| Oct 17, 2017 |
Jan Sieber
(University of Exeter) |
Smooth center manifolds for delay-differential equations |
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Abstract: Delay-differential equations (DDEs) with state-dependent delays
are, as far as is known, at best continuously differentiable once as
dynamical systems. That is, the time-t map does not depend on its argument
with a higher degree of smoothness than 1. However, as I will show, center
manifolds near equilibria are still as smooth as expected from the spectral
gap and from the smoothness of coefficients. In particular, I will review
what precisely "smoothness of coefficients" means.
|
| Oct 24, 2017 |
Carlos Rocha
(Instituto Superior Técnico of Lisbon) |
Global Attractors for Non-autonomous Systems |
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We survey the notions of global attractors for non-autonomous systems, and consider small non-autonomous perturbations of dynamical systems to discuss the resulting changes on the global attractors. We review the notion of Morse-Smale dynamical system and extend this notion to the non-autonomous framework, based on a recent joint work with R. Czaja and W. Oliva.
|
| Nov 7, 2017 |
Preparation SFB 910 |
| Nov 14, 2017 |
Preparation SFB 910 |
| Nov 21, 2017 |
Nikita Begun
(Saint Petersburg State University) |
Chaos for the saw map |
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We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such a map occurs as the Poincare map of simple two-dimensional discrete time piecewise linear systems involving a saturation function. Alternatively, these systems can be viewed as systems with a feedback loop containing the hysteretic stop operator. We analyze chaotic sets and attractors of the ''saw map'' depending on its parameters.
|
| Nov 28, 2017 |
Preparation SFB 910 |
| Dec 5, 2017 |
Preparation SFB 910 |
| Jan 16, 2018 |
Jia-Yuan Dai
(Freie Universität Berlin) |
Existence of local solutions of Gowdy spacetimes |
We consider a class of Gowdy spacetimes that reduces the Einstein's field equation to a system of two semilinear wave equations, by assuming a universe without matter, in which the gravitational wave fronts repeat in space and are mutually parallel. To prove the existence of local solutions of the system, we add a linear perturbation and seek periodic-in-space solutions. The idea of the proof is to apply the Lyapunov-Schmidt reduction. We will solve a related small-divisor problem and discuss how to design the correct functional setting that fits to the nonlinearity.
This ongoing research is a joint work with Dr. Hannes Stuke.
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| Feb 13, 2018 |
Marek Fila
(Comenius University, Bratislava) |
A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation
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We discuss a Gagliardo-Nirenberg-type inequality for functions with fast decay. We use this inequality to derive upper bounds for the decay rates of solutions of a degenerate parabolic equation. Moreover, we show that these upper bounds, hence also the Gagliardo-Nirenberg-type inequality, are sharp in an appropriate sense.
The talk will consist of two parts - an introduction of one hour and a presentation of proofs of also one hour.
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Last change: Feb. 8, 2018
