Public defense in mathematics with Pernilla Johnsen

Time: 17 November at 9.30 – 12.00.

Location: Mid Sweden University, Campus Östersund, room Q221 and digitally via Zoom.

Title of the thesis: 

 "Multiscale Convergence Methods and Homogenization of Partial Differential Equations with Rapid Oscillations"

Respondent: Pernilla Johnsen

Opponent: Associate Professor Irina Pettersson, Chalmers University of Technology

Supervisors: Associate Professor Liselott Flodén, Mid Sweden University

Assistant supervisor:

Associate Professor Marianne Olsson Lindberg, Mid Sweden University

Senior Lecturer Jens Persson, Mid Sweden University

Professor Niklas Wellander, Swedish Defence Research Agency (FOI) and Luleå University of Technology (LTU)

Examination Board:

Professor Anna-Karin Thornberg, KTH

Professor Adrian Muntean, Karlstad University

Associate Professor Magnus Ögren, Örebro University

Participate via Zoom

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.

Link to the thesis in Diva