A simple model for motion of bubbles on obstacles is given by a free
boundary problem of parabolic or hyperbolic type. In this talk, a method
of analysis of such equations based on time semi-discretization will be
presented, which allows direct application to numerical approximation.
Moreover, this method seems promising in studying hyperbolic free
boundary problems, a field with almost no established theory. An example
of such an application will be explained. Extension to the more general
vector-valued case will also be mentioned.

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