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The viscous regularization of an ill-posed diffusion equation with bistablenonlinearity predicts a hysteretic behavior of dynamical phase transitions buta complete mathematical \mbox{understanding} of the intricate multiscaleevolution is still missing. We shed light on the fine structure of\mbox{propagating} phase boundaries by carefully examining traveling wavesolutions in a special case. Assuming a trilinear constitutive relation wecharacterize all waves that possess a monotone \mbox{profile} and connect thetwo phases by a single interface of positive width. We further study the twosharp-interface regimes related to either vanishing viscosity or the bilinearlimit.

Traveling phase interfaces in viscous forward-backward diffusion equations