Geodesic
Polygonal Hele–Shaw problem with surface tension
Masato Kimura1 ; Daisuke Tagami2 ; Shigetoshi Yazaki3
1Kanazawa University, Japan
2Kyushu University, Fukuoka, Japan
3Meiji University, Kanagawa, Japan
Interfaces and free boundaries, Tome 15 (2013) no. 1, pp. 77-93

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DOI

We study a polygonal analogue of the Hele–Shaw moving boundary problem 1 with surface tension based on a framework of polygonal motion proposed by Benesˇ et al. [5]. A key idea is to introduce a polygonal Dirichlet-to-Neumann map. We study variational properties of the polygonal Dirichlet to-Neumann map and show that our polygonal Hele–Shaw problem is a polygonal analogue of the original problem. Local solvability of a polygonal Hele–Shaw problem is also proved by means of the variational structure.
DOI : 10.4171/ifb/295
Classification : 35-XX, 76-XX, 53-XX, 00-XX
Mots-clés : Motion of polygons; moving boundary problem; polygonal Hele–Shaw problem; variational structure; Dirichlet-to-Neumann map, local solvability

Masato Kimura  1   ; Daisuke Tagami  2   ; Shigetoshi Yazaki  3

1 Kanazawa University, Japan
2 Kyushu University, Fukuoka, Japan
3 Meiji University, Kanagawa, Japan 
Masato Kimura; Daisuke Tagami; Shigetoshi Yazaki. Polygonal Hele–Shaw problem with surface tension. Interfaces and free boundaries, Tome 15 (2013) no. 1, pp. 77-93. doi: 10.4171/ifb/295
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     title = {Polygonal {Hele{\textendash}Shaw} problem with surface tension},
     journal = {Interfaces and free boundaries},
     pages = {77--93},
     year = {2013},
     volume = {15},
     number = {1},
     doi = {10.4171/ifb/295},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/295/}
}
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