Blow-up and extinction for a thin-film equation with initial-boundary value conditions

In this paper, we consider an initial-boundary value problem for a thin-film equation, with the nonlocal source |u|q−⨍Ω|u|qdx|u|q−⨍Ω|u|qdx in a bounded domain. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions. Further, we obtain the conditions under which the global solutions extinct in finite time and study the asymptotic behavior of the non-extinct solutions.