We consider a conserved phase-field system with thermal memory on a tridimensional bounded domain. Assuming that the nonlinearity is real analytic, we use a Lojasiewicz-Simon type inequality to study the convergence to steady states of single trajectories. We also give an estimate of the convergence rate.
Submitted November 28, 2007. Published February 22, 2008.
Math Subject Classifications: 35B40, 35B41, 80A22.
Key Words: Conserved phase-field models; memory effects; Lojasiewicz-Simon inequality; steady states; global attractor.
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| Gianluca Mola |
Dipartimento di Matematica "F. Brioschi", Politecnico di Milano
Via Bonardi 9, I-20133 Milano, Italy.
Department of Applied Physics, Graduate School of Engineering
Osaka University, Suita, Osaka 565-0871, Japan
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