Asymptotic behavior of solutions in nonlinear dynamic elasticity (Q1355003)

The asymptotic behavior of a 2D nonlinear elastic system (nonlinear plate with nonlinear internal damping) is studied. The authors are interested in the following problem: How and to which extent can one maximize the margin of stability by introducing suitable large damping? A quantitative statement describing the balance between static and dynamic properties of this nonlinear plate model, in regard to maximization of stability properties, is formulated in a theorem. The asymptotic behavior of the plate model in the case of load attached to the plate is analysed. It is shown that all solutions are attracted by a global and compact attractor.