Blow up threshold for a parabolic type equation involving space integral and variational structure

In this paper, we study a parabolic type equation involving space integrals on a bounded smooth domain. First, using the Banach fixed point theorem, we establish the well-posedness in Lebesgue spaces. Then, with the help of Nehari functional, we find the threshold of the initial data such that the solution either exists globally or blows up in finite time.