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TZID:Europe/Vienna
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DTSTART:20210328T030000
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DTSTAMP:20260404T001912Z
UID:1610445600@ist.ac.at
DTSTART:20210112T110000
DTEND:20210112T130000
DESCRIPTION:Speaker: Maximilian Moser\nhosted by Julian Fischer\nAbstract: 
 In the first part of the talk I will give a general introduction to sharp 
 interface limits for diffuse interface models. Briefly described\, these m
 odels involve a smooth order parameter that is used to distinguish distinc
 t phases/components of a material/fluid in applications. Moreover\, diffus
 e interface models typically contain a small parameter proportional to the
  thickness of transition regions (diffuse interfaces) between phases/compo
 nents. Formally\, by sending this parameter to zero\, one obtains a sharp 
 interface model\, where the interface is described by an evolving hypersur
 face. Such limits are therefore called “sharp interface limits”. Then 
 I will consider the Allen-Cahn equation as a diffuse interface model. The 
 latter can be used for example to describe antiphase boundaries in iron al
 loys. These appear when hot metal is cooling and starts to solidify. The s
 harp interface limit is known to be Mean Curvature Flow. I will give an ov
 erview for rigorous results in this direction. For the remainder of the ta
 lk I will focus on results from my PhD thesis which are rigorous local in 
 time sharp interface limit results for the Allen-Cahn equation and some va
 riants. The novelty here is the consideration of boundary contact for the 
 diffuse interfaces within the method of de Mottoni and Schatzman for sharp
  interface limits. This method works as long as a smooth solution to the l
 imit problem exists. Based on the latter\, one constructs an approximate s
 olution to the diffuse interace model using asymptotic expansions. Then th
 e difference of the exact and approximate solution is estimated with a Gro
 nwall-type argument using a spectral estimate for the associated linear op
 erator.
LOCATION:online via Zoom\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Maximilian Moser: Sharp Interface Limits for Diffuse Interface Mode
 ls with Contact Angle
URL:https://talks-calendar.ista.ac.at/events/3023
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