In this paper, we study the local well-posedness for the Cauchy problem of a semilinear fractional diffusion equation where the perturbations behave like [Formula: see text] and [Formula: see text], and [Formula: see text] is the characteristic function of a ball [Formula: see text]. Here, we are interested in the solvability of the problem when singular initial data [Formula: see text] are taken in [Formula: see text]. Eventually, we give sufficient conditions to the nonexistence of positive global solutions.
In this paper we study local existence, uniqueness, and continuous dependence of an abstract integrodifferential equation. We also present a result on unique continuation and a blow‐up alternative for mild solutions of the integrodifferential equation. Finally, we apply our results to an interesting strongly damped plate equation with memory.
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