Solutions for the Cahn-Hilliard equation with many boundary spike layers. (Q2710424)

The authors study the problem NEWLINE\[NEWLINE\varepsilon^2\Delta v-mv+h(v)-\frac{1}{|\Omega|}\int_\Omega h(v)\,dx= 0\text{ in }\Omega, \quad\frac {\partial v}{\partial\nu} =0\text{ on }\partial\Omega\tag{1}NEWLINE\]NEWLINE and obtain the existence of boundary \(K\)-spike solutions of (1) for any positive integer \(K\) in any smooth bounded domain. They derive a reduction of the energy to finite dimensions, where the variables are closely related to the peak locations.