Asymptotic behavior for a fourth-order parabolic equation modeling thin film growth

The main goal of this work is to study a fourth-order parabolic equation with nonstandard growth conditions. For non-positive initial energy J(u0)≤0, by using the concavity method, we establish that weak solutions blow up in finite time. On the other hand, we also derive the blow-up time estimate and the asymptotic behavior of weak solutions.