Disputation i matematik med Pernilla Johnsen
Välkommen till disputation i matematik med Pernilla Johnsen, som kommer att försvara sin avhandling ”Multiscale Convergence Methods and Homogenization of Partial Differential Equations with Rapid Oscillations”.
Tid: 17 november kl 9.30 – 12.00.
Plats: Mittuniversitetet, Campus Östersund, rum Q221 och digitalt via Zoom.
Avhandlingens titel:
”Multiscale Convergence Methods and Homogenization of Partial Differential Equations with Rapid Oscillations”
Respondent: Pernilla Johnsen
Opponent: Docent Irina Pettersson, Chalmers tekniska högskola
Handledare: Docent Liselott Flodén, Mittuniversitetet
Biträdande handledare:
Docent Marianne Olsson Lindberg, Mittuniversitetet
Lektor Jens Persson, Mittuniversitetet
Professor Niklas Wellander, Totalförsvarets forskningsinstitut (FOI) och Luleå tekniska universitet (LTU)
Betygsnämnd:
Professor Anna-Karin Thornberg, KTH
Professor Adrian Muntean, Karlstads universitet
Docent Magnus Ögren, Örebro universitet
Abstract:
This thesis treats homogenization of partial differential equations with rapid oscillations using multiscale convergence methods. We consider problems with multiple microscopic scales, both spatial and temporal. More precisely, we homogenize linear parabolic problems with a coefficient in front of the temporal derivative that vanishes in the limit, a linear hyperbolic-parabolic problem and monotone parabolic problems. We use evolution settings of multiscale and very weak multiscale convergence, which are methods related to the classical concept of two-scale convergence. We also consider connections between two-scale convergence and the periodic unfolding method, using the concept of general two-scale convergence as a unifying bridge.