Periodicity and Uniqueness of Global Minimizers of an Energy Functional Containing a Long-Range Interaction

Source abstract

We consider, on an interval of arbitrary length, global minimizers of a class of energy functionals containing a small parameter $\varepsilon$ and a long-range interaction. Such functionals arise from models for phase separation in diblock copolymers and from stationary solutions of FitzHugh--Nagumo systems. We show that every global minimizer is periodic with a period of order $\varepsilon^{1/3}$. Also, we identify the number of global minimizers and provide asymptotic expansions for the periods and global minimizers.