%0 Journal Article
%T Finite-dimensional global attractor for a nonlocal phase-field system
%A Maurizio Grasselli
%J Mathematics
%D 2011
%I arXiv
%X We analyze a phase-field system where the energy balance equation is linearly coupled with a nonlinear and nonlocal ODE for the order parameter $\chi$. The latter equation is characterized by a space convolution term which models particle interaction and a singular configuration potential that forces $\chi$ to take values in $(-1,1)$. We prove that the corresponding dynamical system has a bounded absorbing set in a suitable phase space. Then we establish the existence of a finite-dimensional global attractor.
%U http://arxiv.org/abs/1108.0314v1