A nonlinear transmission problem for a compound plate with thermoelastic part

TL;DR

This paper investigates a nonlinear transmission problem involving a composite plate with thermoelastic and isothermal parts, establishing the system's asymptotic behavior and existence of a global attractor under certain nonlinearities.

Contribution

It proves the asymptotic smoothness of the dynamical system and demonstrates the existence of a compact global attractor for specific nonlinearities.

Findings

Dynamical system generated by the problem is asymptotically smooth.

Existence of a compact global attractor is established for Berger type or scalar nonlinearities.

The analysis applies to a coupled thermoelastic-isothermal plate model.

Abstract

In this paper we study a nonlinear transmission problem for a plate which consists of thermoelastic and isothermal parts. The problem generates a dynamical system in a suitable Hilbert space. Main result is the proof of the asymptotic smoothness of this dynamical system. Also we prove the existence of a compact global attractor in particular cases when the nonlinearity is of Berger type or scalar.