Abstract
For a singularly perturbed equation of inhomogeneous Allen-Cahn type with positive potential function in high dimensional general domain, we prove the existence of solutions, at least for some sequence of the positive parameter, which have clustered phase transition layers with mass centered close to a smooth closed stationary and non-degenerate hypersurface. Moreover, the interaction between neighboring layers is governed by a type of Jacobi-Toda system.
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