JournalsifbVol. 23, No. 4pp. 485–506

A free boundary problem for binary fluids

  • Roberto Benzi

    Università di Roma “Tor Vergata”, Italy

  • Michiel Bertsch

    Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, Roma, Italy; Università di Roma Tor Vergata

  • Francesco Deangelis

    Università di Roma “Tor Vergata”; Gran Sasso Science Institute, L’Aquila, Italy
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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.

Cite this article

Roberto Benzi, Michiel Bertsch, Francesco Deangelis, A free boundary problem for binary fluids. Interfaces Free Bound. 23 (2021), no. 4, pp. 485–506

DOI 10.4171/IFB/462