A nonlocal Kirchhoff diffusion problem with singular potential and logarithmic nonlinearity

In this paper, we investigate the following fractional Kirchhoff-type pseudo parabolic equation driven by a nonlocal integro- differential operator L-K: u(t)/vertical bar x vertical bar|(s) + M([u](s)(2))L (K)u + L (K)u(t) = vertical bar u vertical bar(p-2)u log vertical bar u vertical bar, where [u](s) represents the Gagliardo seminorm of u. Instead of imposing specific assumptions on the Kirchhoff function, we introduce a more general sense to establish the local existence ofweak solutions. Moreover, via the sharp fractional Hardy inequality, the decay estimates for global weak solutions, the blow-up criterion, blow-up rate, and the upper and lower bounds of the blow-up time are derived. Lastly, we discuss the global existence and finite time blow-up results with high initial energy.