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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.

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
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