Synchronization phenomena in thermoelastic waves connected in parallel

Abstract

In this paper, the phenomenon of synchronization in nonlinearly coupled thermoelastic waves is investigated. The existence of a finite-dimensional smooth global attractor A α is proven in the natural energy space, where α is the coupling parameter. It is also proved that the coupled thermoelastic wave system can be reduced to a single thermoelastic wave when α tends to infinity. Subsequently, the upper-semicontinuity of their attractors is proven as α → ∞ . These results are ultimately employed to establish the synchronization phenomena for coupled thermoelastic waves. To the best of our knowledge, the synchronization of thermoelastic waves has not been considered before.