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Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory. (English) Zbl 1192.35021

Summary: We consider one-dimensional problem for the thermoelastic diffusion theory and we obtain polynomial decay estimates. Then, we show that the solution decays exponentially to zero as time goes to infinity; that is, denoting by \(E(t)\) the first-order energy of the system, we show that positive constants \(C_{0}\) and \(c_{0}\) exist which satisfy \(E(t) \leq C_{0}E(0)e^{-c_{0}t}\).

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
74H55 Stability of dynamical problems in solid mechanics
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