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Construction of approximate solution to a hyperbolic free boundary problem with volume constraint and its numerical computation. (English) Zbl 1122.35159
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.

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