Yamazaki, Takashi; Omata, Seiro; Svadlenka, Karel; Ohara, Katsuyoshi Construction of approximate solution to a hyperbolic free boundary problem with volume constraint and its numerical computation. (English) Zbl 1122.35159 Adv. Math. Sci. Appl. 16, No. 1, 57-67 (2006). The authors develop a numerical method for bubble motion with free boundary and volume constraint. The model equation becomes a free boundary problem of degenerate hyperbolic type with volume conservation. The notion of a weak solution to this problem is introduced and justified. A minimizing method using the discrete Morse flow of hyperbolic type works well in the numerical solution of this problem. Reviewer: Qin Mengzhao (Beijing) Cited in 6 Documents MSC: 35R35 Free boundary problems for PDEs 35L80 Degenerate hyperbolic equations 49M25 Discrete approximations in optimal control 35L20 Initial-boundary value problems for second-order hyperbolic equations Keywords:bubble motion; discrete Morse flow of hyperbolic type PDF BibTeX XML Cite \textit{T. Yamazaki} et al., Adv. Math. Sci. Appl. 16, No. 1, 57--67 (2006; Zbl 1122.35159)