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Session 24. Nonlinear PDEs with applications in materials science and biology
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Variational analysis of a mesoscale model for bilayer membranes |
Matthias Röger, Technische Universität Dortmund, Germany
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The talk is based on the joint work with Luca Lussardi (Brescia) and Mark Peletier (Eindhoven)
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We present an asymptotic analysis of a mesoscale energy for biological membranes that has been introduced and analyzed in two space dimensions in previous work [1]. The energy is both non-local and non-convex. It combines a surface area and a Monge--Kantorovich-distance term, leading to a competition between preferences for maximally concentrated and maximally dispersed configurations. Here we consider the three-dimensional case and identify a curvature energy of Canham--Helfrich type in the zero-thi
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References- M. A. Peletier and M. Röger,
Partial localization, lipid bilayers, and the elastica functional ,
Arch. Ration. Mech. Anal., 193, 2009, 475-537.
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