Geodesic
A free boundary problem for binary fluids
Roberto Benzi1 ; Michiel Bertsch2 ; Francesco Deangelis3
1Università di Roma “Tor Vergata”, Italy
2Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, Roma, Italy; Università di Roma Tor Vergata
3Università di Roma “Tor Vergata”; Gran Sasso Science Institute, L’Aquila, Italy
Interfaces and free boundaries, Tome 23 (2021) no. 4, pp. 485-506

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DOI

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.
DOI : 10.4171/ifb/462
Classification : 35-XX
Mots-clés : Degenerate parabolic equation, interface, singular perturbation, binary fluid

Roberto Benzi  1   ; Michiel Bertsch  2   ; Francesco Deangelis  3

1 Università di Roma “Tor Vergata”, Italy
2 Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, Roma, Italy; Università di Roma Tor Vergata
3 Università di Roma “Tor Vergata”; Gran Sasso Science Institute, L’Aquila, Italy 
Roberto Benzi; Michiel Bertsch; Francesco Deangelis. A free boundary problem for binary fluids. Interfaces and free boundaries, Tome 23 (2021) no. 4, pp. 485-506. doi: 10.4171/ifb/462
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