On the Cauchy problem for the full von Kármán system (Q1363125)

The existence and uniqueness of a finite energy solution of a semilinear system of hyperbolic equations (the full dynamic von Kármán system) which is modeling the free vibrations of an elastic plate are studied. The global existence and uniqueness of finite energy solutions for an infinite plate are proven and it is shown that the obtained result holds for the case of a rectangular plate which is simply supported or clamped at its edges. It is pointed out that the finite energy solutions of the full dynamic von Kármán system depend continuously on the initial data.