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On the dissipativity of a hyperbolic phase-field system with memory

✍ Scribed by M. Grasselli; V. Pata

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
490 KB
Volume
47
Category
Article
ISSN
0362-546X

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✦ Synopsis

A phase-field system with memory characterized by a heat conduction law of GurtinPipkin type is considered. This model has been already studied by several authors who have obtained various well-posedness results. The longterm behavior of a single solution has also been investigated. In this note we first formulate the model as a dynamical system in a suitable phase space which accounts for the whole past history of the temperature. Then we prove the existence of a (uniform) absorbing set which basically shows the dissipative nature of the system. Existence of a compact attractor is discussed as well.

πŸ“œ SIMILAR VOLUMES

Attractor for a conserved phase-field sy
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## Abstract We consider a conserved phase‐field system of Caginalp type, characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient, respectively. The latter dependence is a law of Gurtin–Pipkin type, so that the eq

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We consider a conserved phase-field system of Caginalp type, characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient, respectively. The model consists of a parabolic integrodifferential equation, coupled with a fo

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## Abstract In this article, we study the long time behavior of a parabolic‐hyperbolic system arising from the theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equat