Solvability and stability of von Karman model without rotational inertia with nonlinear forces

Abstract

We investigate the nonlinear oscillations of plates described by von Karman evolution equations with mixed–hinged/simply supported nonlinear boundary conditions. The von Karman evolution system is of “hyperbolic type” with nonlinear transverse and boundary forces. We prove the existence of global solution (on given interval) constructing new variational approach to that system. We do not prove the Hadamard well-posedness, however a kind of new dependence of solutions on initial data is considered.