A sixth-order thin film equation in two space dimensions

Abstract

In this article, the author studies the weak solutions for a sixth-order thin film equation in two space dimensions, which arises in the industrial application of the isolation oxidation of silicon. Based on the Schauder type estimates, we establish the global existence of classical solutions for regularized problems. Our approach lies in the combination of the energy techniques with some methods based on the framework of Campanato spaces. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions in two space dimensions. The nonnegativity of solutions is also discussed.