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Asymptotic behaviour and exponential stability for thermoelastic problem with localized damping. (English) Zbl 1231.47038

Summary: A semi-linear thermoelastic problem with localized damping is considered, which is one of the most important mathematical models in material science. The existence and decays exponentially to zero of solution of this problem are obtained. Moreover, the existence of absorbing sets is achieved in the non-homogeneous case. The result indicates that the system which we studied here is asymptotic stability.

MSC:

47D06 One-parameter semigroups and linear evolution equations
34G10 Linear differential equations in abstract spaces
35B35 Stability in context of PDEs
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