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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Dynamics of linearized cosmological perturbations
- Alan Rendall (AEI\, Potsdam)
DTSTART;TZID=Europe/London:20090309T160000
DTEND;TZID=Europe/London:20090309T170000
UID:TALK17040AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/17040
DESCRIPTION:In cosmology an important role is played by homoge
neous and isotropic solutions of the Einstein-Eule
r equations and linearized perturbations of these.
In this talk I present results of Paul Allen and
myself on the asymptotic behaviour of certain line
arized solutions (so-called 'scalar perturbations'
) both in the approach to the initial singularity
and at late times. The main equation of interest i
s a linear hyperbolic equation whose coefficients
depend only on time. Expansions for the solutions
are obtained in both asymptotic regimes. In both c
ases it is shown how general solutions can be para
metrized by certain functions which are coefficien
ts in the asymptotic expansion. The central techni
que in the proofs is that of energy estimates. An
interesting feature of the results is a bifurcatio
n observed in the late-time asymptotics for an asy
mptotically polytropic equation of state\, occurri
ng for the polytropic index corresponding to a rad
iation fluid.
LOCATION:CMS\, MR13
CONTACT:Prof. Mihalis Dafermos
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