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Copolymer-homopolymer blends: global energy minimisation and global energy bounds. (English) Zbl 1191.49006

Summary: We study a variational model for a diblock copolymer-homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta-Kawasaki energy. In one dimension, on the real line and on the torus, we prove existence of minimisers of this functional and we describe in complete detail the structure and energy of stationary points. Furthermore we characterise the conditions under which the minimisers may be non-unique. In higher dimensions we construct lower and upper bounds on the energy of minimisers, and explicitly compute the energy of spherically symmetric configurations.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
82D60 Statistical mechanics of polymers
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
49N90 Applications of optimal control and differential games
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