JournalsifbVol. 15, No. 1pp. 77–93

Polygonal Hele–Shaw problem with surface tension

  • Masato Kimura

    Kanazawa University, Japan
  • Daisuke Tagami

    Kyushu University, Fukuoka, Japan
  • Shigetoshi Yazaki

    Meiji University, Kanagawa, Japan
Polygonal Hele–Shaw problem with surface tension cover
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Abstract

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.

Cite this article

Masato Kimura, Daisuke Tagami, Shigetoshi Yazaki, Polygonal Hele–Shaw problem with surface tension. Interfaces Free Bound. 15 (2013), no. 1, pp. 77–93

DOI 10.4171/IFB/295