Global existence blow up and extinction for a class of thin-film equation

In this paper we use the modified method of potential wells to study the properties of solutions for a class of higher order nonlinear parabolic equations with p-Laplace term −(|ux|p−2ux)x and nonlocal source |u|q−1u−1∣Ω∣∫Ω|u|q−1udx. Global existence, uniqueness, blow up in finite time and asymptotic behavior of solutions will be proved under different initial conditions. Furthermore, a numerical example is given to illustrate the blow-up of solutions in finite time.