Clustering phase transition layers with boundary intersection for an inhomogeneous Allen-Cahn equation
Clustering phase transition layers with boundary intersection for an inhomogeneous Allen-Cahn equation
We consider the nonlinear problem of inhomogeneous Allen-Cahn equation \begin{document}$ \epsilon^2\Delta u+V(y)\,(1-u^2)\,u = 0\quad \mbox{in}\ \Omega, \qquad \frac {\partial u}{\partial \nu} = 0\quad \mbox{on}\ \partial \Omega, $\end{document} where $ \Omega $ is a bounded domain in $ \mathbb R^2 $ with smooth boundary, $ \epsilon $ is a small positive …