<div class="csl-bib-body">
<div class="csl-entry">Daus, E. S. (2016). <i>Analysis of kinetic and diffusive multi-species systems</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2016.37890</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2016.37890
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/3314
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dc.description
Zusammenfassung in deutscher Sprache
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
The objective of this thesis is the analysis of kinetic and diffusive multi-species systems with certain cross effects between the species, which are very important in many applications in physics, biology and chemistry. In the first part of this thesis, we study the multi-species Boltzmann equation for hard potentials or Maxwellian molecules under Grad's angular cut-off condition on the torus, which describes the evolution of a dilute gaseous mixture. First, we work on the linearized level with same molar masses, where we prove a multi-species spectral-gap estimate of the collision operator, which leads to exponential trend to global equilibrium using the hypocoercive properties of the linearized Boltzmann equation. Next, we study the full Cauchy theory of the nonlinear multi-species Boltzmann equation close to global equilibrium for different molar masses in physically relevant function spaces, recovering the optimal physical threshold in the particular case of a multi-species hard spheres mixture with same molar masses. The second part of this thesis is devoted to cross-diffusion systems. First, we prove global existence of weak solutions for a generalized SKT cross-diffusion population dynamics model with an arbitrary number of species under detailed balance or weak cross-diffusion condition using entropy methods. Finally, we study a rigorous fast-reaction limit from reaction-diffusion systems to cross-diffusion systems using entropy estimates and additional duality estimates. Since the reaction-diffusion system exhibits an entropy structure, performing the fast-reaction limit leads to a limiting entropy of the limiting cross-diffusion system. In this way, we obtain new entropies for new classes of cross-diffusion systems.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Boltzmann-Gleichung
de
dc.subject
Populationsdynamik
de
dc.subject
Entropiemethode
de
dc.subject
Boltzmann equation
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dc.subject
population dynamics
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dc.subject
entropy method
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dc.title
Analysis of kinetic and diffusive multi-species systems
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dc.title.alternative
Kinetische und diffusive Gleichungen für Multikomponentensystems
de
dc.type
Thesis
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dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2016.37890
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Esther Sarah Daus
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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dc.type.qualificationlevel
Doctoral
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dc.identifier.libraryid
AC13350640
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dc.description.numberOfPages
212
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-7297
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_db06
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item.languageiso639-1
en
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item.openaccessfulltext
Open Access
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item.openairetype
doctoral thesis
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item.grantfulltext
open
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crisitem.author.dept
E101-01 - Forschungsbereich Analysis
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crisitem.author.parentorg
E101 - Institut für Analysis und Scientific Computing