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Hysteresis and phase transitions in a lattice regularization of an ill-posed forward-backward diffusion equation

We consider a lattice regularization for an ill-posed diffusion equation with trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

preprint2017arXivOpen access
Michael HelmersMichael Herrmann
math.APmath.DS
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Michael HelmersMichael Herrmann

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