
arXiv: 2207.01757
We investigate the Cauchy problem for the thermoelastic plate system associated with Newton’s law of cooling, where optimal growth ( n ⩽ 4 n\leqslant 4 ) or decay ( n ⩾ 5 n\geqslant 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.
Cauchy problem, PDEs in connection with classical thermodynamics and heat transfer, Initial value problems for systems of linear higher-order PDEs, Asymptotic behavior of solutions to PDEs, lower-order term, parabolic-hyperbolic system, Mathematics - Analysis of PDEs, thermoelastic plate system, FOS: Mathematics, optimal estimate, asymptotic profile, Analysis of PDEs (math.AP)
Cauchy problem, PDEs in connection with classical thermodynamics and heat transfer, Initial value problems for systems of linear higher-order PDEs, Asymptotic behavior of solutions to PDEs, lower-order term, parabolic-hyperbolic system, Mathematics - Analysis of PDEs, thermoelastic plate system, FOS: Mathematics, optimal estimate, asymptotic profile, Analysis of PDEs (math.AP)
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