ROBUST EXPONENTIAL ATTRACTORS FOR SINGULARLY PERTURBED PHASE-FIELD TYPE EQUATIONS

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Invariant Manifolds for Physical and Chemical Kinetics (2005, background): “The operator −ν42 effectively suppresses the short waves (with the logarithmic decrement ∼ k for the wave vector k); it allows to prove the existence of the finite–dimensional attractors and to estimate their dimensions for various hypothesis about f and boundary conditions [325–329].”
On the Caginalp system with dynamic boundary conditions and singular potentials (2009, background): “[ 24 ],[33]andthereferencestherein. Inparticular,onehas satisfactoryresultsonthe existence and uniqueness of solutions, the existence offinite dimensional attractors and the convergence of solutions to steady states.”
Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, result): “(d) Based on the above results, one has been able to prove the existence of exponential attractors in many situations, see [6,7,60,61,68,70,71,74,85,100–103,105–109,116, 117,157,175–177,184], and [216].”