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A discrete convolution model for phase transitions. (English) Zbl 0956.74037
Summary: We study a discrete convolution model for Ising-like phase transitions. This nonlocal model is derived as an \(l_2\)-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.

MSC:
74N20 Dynamics of phase boundaries in solids
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
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