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

    loading  Checking for direct PDF access through Ovid


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.

    loading  Loading Related Articles