FINITE-DIMENSIONAL GLOBAL ATTRACTOR FOR A NONLOCAL PHASE-FIELD SYSTEM

Abstract

We analyze a phase-field system where the energy balance equation is lin-early coupled with a nonlinear and nonlocal ODE for the order parameter χ. The latter equation is characterized by a space convolution term which models long-range inter-actions and a singular configuration potential that forces χ to take values in the interval (−1, 1). We prove that the corresponding dynamical system is dissipative, i.e., it has a bounded absorbing set in a suitable phase space. Then we establish the existence of a finite-dimensional global attractor.