Mathematisches Kolloquium: Diffuse Interface Models and their Sharp Interface Limits
Wann
Donnerstag, 31. Oktober 2024
17 bis 0 Uhr
Wo
G201
Veranstaltet von
Vortragende Person/Vortragende Personen:
Prof. Dr. Helmut Abels (Universität Regensburg)
Abstract: Interfaces separating two or more species or components of a material are omnipresent in applications in the sciences. Nowadays there are two main classes of models to describe interfaces, both from a theoretical and practical point of view: In classical so-called "sharp interface models" the species or components under consideration fill
disjoint domains that are separated by lower dimensional surfaces of a certain regularity. On the other hand in "diffuse interface models" a partial mixing of the species or components on a small length scale is taken into account, which leads to an interfatial layer of small but positive thickness. This has the advantage that the interfaces do not need to be resolved explicitly and singularities in the interfaces can be described consistently. In this talk we will give an overview of some basic diffuse interface models with applications to material sciences and fluid mechanics. Moreover, we will discuss some analytic results on the relation between diffuse and sharp interface models, when the interfatial thickness of the diffuse interface tends to zero.