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A free boundary problem for binary fluids

Roberto Benzi,Michiel Bertsch, Francesco Deangelis

INTERFACES AND FREE BOUNDARIES（2021）

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Abstract
A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to a singular perturbation problem for a strongly degenerate parabolic partial differential equation in 1D. We present a conjecture for an asymptotic formula for the velocity of the free boundary and prove a weak version of the conjecture. The results are based on the analysis of a family of local travelling wave solutions.
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Key words
Degenerate parabolic equation,interface,singular perturbation,binary fluid
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