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This volume is devoted to the study of hyperbolic free boundary
problems possessing variational structure. Such problems can be
used to model, among others, oscillatory motion of a droplet on a
surface or bouncing of an elastic body against a rigid obstacle. In
the case of the droplet, for example, the membrane surrounding the
fluid in general forms a positive contact angle with the obstacle,
and therefore the second derivative is only a measure at the
contact free boundary set. We will show how to derive the
mathematical problem for a few physical systems starting from the
action functional, discuss the mathematical theory, and introduce
methods for its numerical solution. The mathematical theory and
numerical methods depart from the classical approaches in that they
are based on semi-discretization in time, which facilitates the
application of the modern theory of calculus of variations.
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