Geodesic
On the existence of mean curvature flow with transport term
Chun Liu1 ; Norifumi Sato2 ; Yoshihiro Tonegawa3 orcid
1The Pennsylvania State University, University Park, USA
2Furano H.S., Furano (Hokkaido), Japan
3Hokkaido University, Sapporo, Japan
Interfaces and free boundaries, Tome 12 (2010) no. 2, pp. 251-277

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DOI

We prove the global-in-time existence of weak solution for a hypersurface evolution problem where the velocity is the sum of the mean curvature and arbitrarily given non-smooth vector field in a suitable Sobolev space. The approximate solution is obtained by the Allen–Cahn equation with transport term. By establishing the density ratio upper bound on the phase boundary measure it is shown that the limiting surface moves with the desired velocity in the sense of Brakke.
DOI : 10.4171/ifb/234
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Mean curvature flow, varifold, Allen–Cahn equation, phase field method

Chun Liu  1   ; Norifumi Sato  2   ; Yoshihiro Tonegawa  3

1 The Pennsylvania State University, University Park, USA
2 Furano H.S., Furano (Hokkaido), Japan
3 Hokkaido University, Sapporo, Japan 
Chun Liu; Norifumi Sato; Yoshihiro Tonegawa. On the existence of mean curvature flow with transport term. Interfaces and free boundaries, Tome 12 (2010) no. 2, pp. 251-277. doi: 10.4171/ifb/234
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     doi = {10.4171/ifb/234},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/234/}
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