% IMPORTANT: The following is UTF-8 encoded. This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.
@PHDTHESIS{Lax:674472,
author = {Lax, Christian},
othercontributors = {Walcher, Sebastian and Frank, Martin},
title = {{A}nalyse und asymptotische {A}nalyse von
{K}ompartimentsystemen},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
reportid = {RWTH-2016-09465},
pages = {1 Online-Ressource (xi, 268 Seiten) : Illustrationen,
Diagramme},
year = {2016},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2016},
abstract = {This thesis deals with singularly disturbed systems of
differential equations. The primary goal is the computation
of asymptotic reductions which help with the analysis of
those systems. The reductions are based on the classical
theories by Tikhonov and Fenichel and thus are referred to
as Tikhonov-Fenichel reductions.The thesis consists of two
parts. The first part discusses autonomous ODEs and focuses
on modelling chemical reactions subjected to quasi steady
state assumptions.Therefore, most of the results refer to
rational or polynomial systems. Building on the work of Lena
Nöthen and Alexandra Goeke, three main results are proven:
First of all, Hoppensteadt's theorem can be generalized to
systems which are not in Tikhonov normal form. Moreover, a
reformulation of the assumptions of the theorem helps to
gain a better applicability. Secondly, we can compute
Tikhonov-Fenichel reductions for all chemical reaction
networks which can be divided into slow and fast reactions,
as long as the fast part consists of weakly reversible
reactions of first order. The third result refers to
compartmental systems, i.e. systems that are governed by
transport between subsystems and interaction within these
subsystems. It turns out that Tikhonov-Fenichel reductions
of those systems can be derived from the individual
interaction terms alone.The second part of the thesis
discusses asymptotic reductions of reaction diffusion
systems. As there is no counterpart to Tikhonov's theorem in
infinite dimensions, the main goal is finding and computing
explicit reductions of reaction diffusion systems (without
giving general convergence results). We do this by
considering spatially discretized reaction-diffusion systems
as compartmental systems. Our method is backed by various
results: First and foremost, we show the consistency of the
proposed reduction. Furthermore, a convergence result is
proved for reaction diffusion systems for which every
reaction is of first order and the fast part satisfies the
principle of detailed balance. Lastly, we discuss some
examples of which the Michaelis-Menten reaction is the most
prominent one. We compare our heuristical reduction of these
examples to known results in the literature and discuss
systems where no previous results seem to be known. In the
latter case, numerical simulations exhibit nice convergence
properties.},
cin = {114110 / 110000},
ddc = {510},
cid = {$I:(DE-82)114110_20140620$ / $I:(DE-82)110000_20140620$},
typ = {PUB:(DE-HGF)11},
urn = {urn:nbn:de:hbz:82-rwth-2016-094653},
doi = {10.18154/RWTH-2016-09465},
url = {https://publications.rwth-aachen.de/record/674472},
}
guest ::