An Integrodifferential Model for Phase Transitions: Stationary Solutions in Higher Space Dimensions |
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| Authors: | Bates Peter W. Chmaj Adam |
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| Affiliation: | (1) Department of Mathematics, Brigham Young University, Provo, Utah, 84602 |
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| Abstract: | 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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| Keywords: | nonlocal Allen– Cahn equation long-range interaction pinning |
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