STABILITY OF EXPONENTIAL ATTRACTORS FOR SINGULARLY PERTURBED PHASE-FIELD SYSTEMS OF OONO TYPE

e consider a phase-field system that takes into account the long-ranged interactions in phase separation based on a theory introduced by Y.Oonoet al .(tau phi t+N(N phi+g(phi)-u) +sigma phi= 0, epsilon ut+phi t+Nu+gamma u= 0,(S epsilon) where tau >0,sigma,gamma >= 0,epsilon is an element of(0,1] is the heat capacity,phi is the order parameter,uis the absolute temperature, and the Laplace operator N=-triangle :D(N)-> L-2(ohm) is subject to either Neumann boundary conditions (in which case ohm subset of R(d )is a bounded domain with smooth boundary) or periodic bound-ary conditions (in which case ohm = Pi di=1(0,Li), Li>0),d= 1,2 or 3. Weconsider a class of nonlinear functions g is an element of C3(R) that contains the polynomialg(phi) =P(2p-1)k=1ak phi k, p is an element of N, p >= 2, a(2p-1)>0. We prove a well-posedness result and the existence of the global attractor which is upper semicontinuousat epsilon= 0. Then we construct a family of exponential attractors that is Holdercontinuous at epsilon= 0. Our present contribution completes and generalizes some recent results proven by Bon foh and Suleman in [Comm. Pure Appl. Anal.2021; 20: 3655-3682] where a conserved model (corresponding to sigma=gamma= 0 in(S epsilon)) that takes into account the viscosity effects in the material was considered