Clustered interior phase transition layers for an inhomogeneous Allen-Cahn equation in higher dimensional domains
Clustered interior phase transition layers for an inhomogeneous Allen-Cahn equation in higher dimensional domains
For a singularly perturbed equation of inhomogeneous Allen-Cahn type with positive potential functionin high dimensional general domain, we prove the existence of solutions,at least for some sequence of the positive parameter,which have clustered phase transition layerswith mass centered close to a smooth closed stationary and non-degenerate hypersurface.Moreover, the interaction between …