CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

18 mai 2021 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Bifurcation Points in the Ohta-Kawasaki Model

Séminaire par Thomas Wanner (George Mason University, USA)

Diblock copolymers are a class of materials formed by the reaction of two linear polymers. The different structures taken on by these polymers grant them special properties, which can prove useful in applications such as the development of new adhesives and asphalt additives. We consider a model for the formation of diblock copolymers first proposed by Ohta and Kawasaki, which is a Cahn-Hilliard-like equation together with a nonlocal term. Unlike the Cahn-Hilliard model, even on one-dimensional spatial domains the steady state bifurcation diagram of the Ohta-Kawasaki model is still not fully understood. We therefore present computer-assisted proof techniques which can be used to validate and continue its bifurcation points. This includes not only fold points, but also pitchfork bifurcations which are the result of a cyclic group action beyond forcing through Z_2 symmetries.