Virginie Ehrlacher (ENPC, Paris): Analysis of cross-diffusion equations in a moving domain

Mittwoch, 14.09.2016 14:15 im Raum SRZ 204
Mathematik und Informatik

Abstract: 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 [1] 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 [2] and developped in [3]. Results about the existence of a weak solution, long time behaviour and optimal control will be presented. (joint work with Athmane Bakhta) [1] A. Jüngel and I.V. Steltzer, "Existence Analysis of Maxwell-Stefan Systems for Multicomponent Mixtures", SIAM J. Math. Anal., 45(4), 2421–2440. [2] M. Burger, M. Di Francesco, "J.-F. Pietschmann and B. Schlake, Nonlinear Cross-Diffusion with Size Exclusion", SIAM J. Math. Anal., 42(6), 2842–2871. [3] A. Jüngel, "The boundedness-by-entropy method for cross-diffusion systems", Nonlinearity, 28(6), 2016.

Angelegt am Dienstag, 06.09.2016 10:48 von mburg_01
Geändert am Dienstag, 06.09.2016 11:47 von mburg_01
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Seminar AG Imaging
Oberseminar Angewandte Mathematik
Angewandte Mathematik Münster