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In this paper we are concerned with local existence, regularity and continuous dependence upon the initial data of $$\epsilon $$ϵ-regular mild solutions for the abstract integrodifferential equation (1, 2). We… Click to show full abstract
In this paper we are concerned with local existence, regularity and continuous dependence upon the initial data of $$\epsilon $$ϵ-regular mild solutions for the abstract integrodifferential equation (1, 2). We also present a result on unique continuation and a blow-up alternative for an $$\epsilon $$ϵ-regular mild solution of (1, 2). Finally, we apply our results to three interesting models: Navier–Stokes equations with memory, diffusion equations with memory and a strongly damped plate equation with memory.
Journal Title: Mathematische Annalen
Year Published: 2017
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