A parabolic equation modeling epitaxial growth of thin film with new growth conditions

Here, we examine a fourth-order parabolic partial differential equation representing the epitaxial thin film growth with a nonlinear function satisfying some advanced growth conditions. Using the modified potential well method, we prove the global existence of solutions for subcritical and critical initial energy. Further, the concavity method is employed to prove the blow-up of solution for negative, subcritical, and critical initial energy, as well as the upper bound for blow-up.