Some dynamical models in which there is a significant interplay between interfacial and bulk degrees of freedom are treated at the mean-field (or Van Hove) level from a coarse-grained microscopic viewpoint. Specifically, the near-equilibrium interfacial dynamics of two of the simplest models with conservation laws, models B and C, are studied with use of (as appropriate) variational techniques, perturbation theory, and (with certain additional simplifications) exact solutions. Use of these

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... ds allows the dispersion relation for interfacial modes to be interpolated between the "hydrodynamical" and critical regimes. The crossover scaling behavior lends support to renormalizationgroup methods near d=1 which focus on the interfacial modes but nonetheless extract the bulk dynamical exponent as well as the crossover.