A better understanding of longtime dynamical properties of infinite dimensional dynamical systems generated by semilinear parabolic PDE's is of paramount relevance. The objective of this proposal is to indicate direction of research tobe pursued which in turn investigate the unbounded attractors associated to such systems under distinct perturbations (singular or not). The aim is to study unbounded attractors under perturbations that make the associated dynamical system dissipative. We also consider the phenomenon of homogenization and rate of convergence of unbounded attractors.
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