Virginie Ehrlacher (ENPC, Paris): Analysis of cross-diffusion equations in a moving domain
Mittwoch, 14.09.2016 14:15 im Raum SRZ 204
The aim of this work is to suggest and analyze a system of equations to model a Physical Vapor Deposition (PVD) process. This process is used for instance for the fabrication of thin film solar cells. A substrate layer is inserted in a hot chamber, where different chemical species are injected under a gaseous form. These different species deposit onto the surface of the substrate, which produces the growth of a thin solid film. Due to the high temperature in the hot chamber, the chemicals also diffuse in the bulk of the solid film.
This diffusion phenomenon is modeled through a system of cross-diffusion equations which is closely related to the Stefan-Maxwell system (see  for instance). The analysis of the obtained model is restricted so far to the one-dimensional case and relies on the so-called boundedness by entropy method which was introduced in  and developped in . Results about the existence of a weak solution, long time behaviour and optimal control will be presented.
(joint work with Athmane Bakhta)
 A. Jüngel and I.V. Steltzer, "Existence Analysis of Maxwell-Stefan Systems for Multicomponent Mixtures", SIAM J. Math. Anal., 45(4), 24212440.
 M. Burger, M. Di Francesco, "J.-F. Pietschmann and B. Schlake, Nonlinear Cross-Diffusion with Size Exclusion", SIAM J. Math. Anal., 42(6), 28422871.
 A. Jüngel, "The boundedness-by-entropy method for cross-diffusion systems", Nonlinearity, 28(6), 2016.