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Vibrations of elastic membranes with moving boundaries. (English) Zbl 1008.74039

The authors investigate a mathematical model for small deformations of a circular membrane when the boundary is not fixed and can move. The theory is based on a wave equation of the form \({\partial^2 u\over \partial t^2}-[a(t)+ b(t)\int_{\Omega_t} |\nabla u(x,t)|^2 dx] \Delta u=0\).

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K15 Membranes
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