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July  2003, 9(4): 949-968. doi: 10.3934/dcds.2003.9.949

Dissipativity of a conserved phase-field system with memory

Federico Mario Vegni 1,

1. 

Dipartimento di Matematica, Università degli Studi di Brescia, Via Valotti, 9 I-25133 Brescia, Italy

Received  July 2001 Revised  October 2002 Published  April 2003

We analyze a conserved phase-field system, characterized by heat memory terms: memory kernels $a$ and $b$ account for relaxation effects in the energy constitutive equation and in the Gurtin-Pipkin heat conduction law, respectively. This model consists of a hyperbolic integrodifferential equation for the temperature $\theta$ coupled with a nonlinear fourth order evolution equation for the phase variable $\chi$. With appropriate initial and boundary data, we prove that the system can be interpreted as a process. We show that it possesses an absorbing set, under three -thermodynamically consistent- conditions on the memory kernel $a$.
Keywords: continuous dependence, materials with memory, existence and uniqueness, nonautonomous dynamical systems, uniform energy estimates, Conserved phase-field models, uniform absorbing set..
Mathematics Subject Classification: 35G25, 45K05, 80A2.
Citation: Federico Mario Vegni. Dissipativity of a conserved phase-field system with memory. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 949-968. doi: 10.3934/dcds.2003.9.949
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