A note on asymptotic profiles for the thermoelastic plate system

We investigate the Cauchy problem for the thermoelastic plate system associated with Newton’s law of cooling, where optimal growth ($n⩽4$) or decay ($n⩾5$) estimates and asymptotic profiles of solutions for large-time are studied. Especially, the additional lower-order term in the temperature equation weakens decay rates of the vertical displacement, and leads to a new leading term comparing with the classical thermoelastic plates.