Traveling phase interfaces in viscous forward-backward diffusion equations

Carina Geldhauser; Michael Herrmann; Dirk Janßen

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arXiv · 2311.11573

Traveling phase interfaces in viscous forward-backward diffusion equations

Carina Geldhauser·Michael Herrmann·Dirk Janßen

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Abstract

The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical \mbox{understanding} of the intricate multiscale evolution is still missing. We shed light on the fine structure of \mbox{propagating} phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone \mbox{profile} and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.

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Carina Geldhauser, Michael Herrmann, Dirk Janßen. 2023-11-20. Traveling phase interfaces in viscous forward-backward diffusion equations. https://arxiv.org/abs/2311.11573

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