Vortragsankündigung

 Im Rahmen des Oberseminars Analysis/Numerik 

spricht

 Herr Alexander Meiners (Universität Oldenburg) 

über 

Bifurcation analysis for geometric PDE’s 

F. Al Saadi, E. Knobloch, A. Meiners, H. Uecker

This talk will broadly cover bifurcation problems within partial differential equations. As an introductory example, we explore bifurcations and stability in a semiconductor model, while reviewing essential concepts in dynamical systems analysis. In particular, we focus on Turing– Hopf mixed modes in the vicinity of codimension-two bifurcation points. The main tool is numerical continuation in pde2path of steady-state and periodic solutions. From that, we consider geometric partial differential equations. Within this broad field, we examine a model for the shape of bilayer membranes—the Helfrich equation. We investigate destabilizing bifurcations from spherical and cylindrical topologies. The spherical case serves as a model for the shape of red blood cells, while the cylindrical case reveals interesting bifurcations into non-axisymmetric solutions. We apply numerical continuation with the Xcont extension of pde2path to both cases to study stability and secondary branches. In the cylindrical case in particular, we also derive amplitude equations to further analyze axisymmetric, nonaxisymmetric and mixed-mode solutions. 

Der Vortrag findet statt am Donnerstag, den 08.05.2025 

um 14.45 – 15.30 Uhr im Raum W01 006 

Interessierte sind herzlich eingeladen. 

Fakultät V Mathematik und Naturwissenschaften