Grandient Estimates for Degenerate Diffusion Equations. I.
On the singular limit in a phase field model of phase transitions
A maximum principle for systems with variational structure and an application to standing waves
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.
Continuum limits of particles interacting via diffusion.
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