Qualitative properties for a sixth–order thin film equation

Abstract

In this article, the author studies the qualitative properties of weak solutions for a sixth‐order thin film equation, 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. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the expansion of the support of solutions are also discussed.

First published online: 10 Feb 2011