Finite-dimensional global attractor for a nonlocal phase-field system

We analyze a phase-field system where the energy balance equation is linearly coupled with a nonlinear and nonlocal ODE for the order parameter $χ$. The latter equation is characterized by a space convolution term which models particle interaction and a singular configuration potential that forces $χ$ 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.

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