An Integrodifferential Model for Phase Transitions: Stationary Solutions in Higher Space Dimensions

We study the existence and stability of stationary solutions of an integrodifferential model for phase transitions, which is a gradient flow for a free energy functional with general nonlocal integrals penalizing spatial nonuniformity. As such, this model is a nonlocal extension of the Allen–Cahn equation, which incorporates long-range interactions. We find that the set of stationary solutions for this model is much larger than that of the Allen–Cahn equation.

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