A note on asymptotic profiles for the thermoelastic plate system

Abstract

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.

References in corpus (2)

• Asymptotic behaviors for the Jordan-Moore-Gibson-Thompson equation in the viscous case
• Optimal large-time estimates and singular limits for thermoelastic plate equations with the Fourier law