asymptotic behaviors of solutions to a singular non-local fourth-order parabolic equation with gradient-type logarithmic nonlinearity

In this paper, we consider the initial-boundary value problem to a singular non-local fourth-order parabolic equation with gradient-type logarithmic nonlinearity. we prove the global existence of weak solutions by utilizing the cut-off function technique and galerkin's approximation method. we establish novel threshold criteria for the finite-time blow-up of solutions with initial value at arbitrary energy levels, and derive explicit upper bounds for the blow-up time under appropriate conditions. furthermore, by employing energy estimates and specific ordinary differential inequalities, we characterize both non-extinction and extinction phenomena of solutions in finite time, and rigorously quantify their corresponding extinction rates.