A Discrete Convolution Model¶for Phase Transitions

Abstract: We study a discrete convolution model for Ising-like phase transitions. This nonlocal model is derived as an l2-gradient flow for a Helmholtz free energy functional with general long range interactions. We construct traveling waves and stationary solutions, and study their uniqueness and stability. In particular, we find some criteria for “propagation” and “pinning”, and compare our results with those for a previously studied continuum convolution model.

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