Abstract
The simplest Ginzburg-Landau model with conservation law is investigated. The initial state is specified by an inhomogeneous profile of the chemical potential associated with the conserved quantity, that is, the mean spin. It is shown that the mean spin satisfies a nonlinear diffusion equation in the hydrodynamic limit. The proof is based on the nice, parabolic structure of the model. A standard perturbation technique is used.
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Fritz, J. On the hydrodynamic limit of a one-dimensional Ginzburg-Landau lattice model. Thea priori bounds. J Stat Phys 47, 551–572 (1987). https://doi.org/10.1007/BF01007526
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DOI: https://doi.org/10.1007/BF01007526