March  2009, 2(1): 1-16. doi: 10.3934/dcdss.2009.2.1

Convergence to equilibria of solutions to a conserved Phase-Field system with memory

1. 

Department of Mathematics, Ohio University, Athens, OH 45701

2. 

Mathematical Institute AV ČR, Žitná 25, 115 67 Praha 1

Received  December 2007 Revised  March 2008 Published  January 2009

We show that the trajectories of a conserved phase-field model with memory are compact in the space of continuous functions and, for an exponential relaxation kernel, we establish the convergence of solutions to a single stationary state as time goes to infinity. In the latter case, we also estimate the rate of decay to equilibrium.
Citation: Sergiu Aizicovici, Hana Petzeltová. Convergence to equilibria of solutions to a conserved Phase-Field system with memory. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 1-16. doi: 10.3934/dcdss.2009.2.1
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