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In this paper, we study the global and pullback attractors for a strongly damped wave equation with delays when the force term belongs to different space. The results following from the solution generate a compact set.
5-Alkenyl-2,2-butylidene-1,3-dioxane-4,6-diones were synthesized by the Knoevenagel condensation reaction of aromatic aldehydes with 2,2-butylidene-1,3-dioxane-4,6-dione using o-phthalimide-N-sulfonic acid as catalyst, without solvent under ultrasonic irradiation. The present method has some notable advantages such as mild reaction conditions, short reaction times, less catalyst dosage and high yields with the green aspects by avoiding toxic catalysts and solvents. Further, the catalyst can be reused for five times without any noticeable decrease in the catalytic activity.