Potomkin M. Asymptotic dynamics of nonlinear elastic plates with memory

Purpose of the work is a description of asymptotic behavior of solutions to nonlinear equations of thermoelastic plate oscillations in different formulations. Object of research is initial-boundary problems of systems of equations of a Berger thermoplastic plate with classic Fourier law of heat conduction, a thermovscoelastic Berger plate with Gurtin-Pipkin law, a compound plate with thermoelastic and elastic parts. The results obtained are new. The main results are the following. For all considered systems the well-posedness result is proved and dynamic systems which possess a compact global attractor are built on their solutions. For thermoelastic and thermoviscoelastic plates regularity, finite-dimensionality and semicontinuity with respect to parameters of attractors and one-to-one property of the evolution operator are proved. Closeness between a solution of the thermoviscoelastic plate and a solution of the corresponding limiting system when relaxation parameters are close to 0 is proved.