Advances in Differential Equations

A sixth-order thin film equation in two space dimensions

Changchun Liu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Adv. Differential Equations, Volume 20, Number 5/6 (2015), 557-580.

First available in Project Euclid: 30 March 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35D05 35K55: Nonlinear parabolic equations 35K65: Degenerate parabolic equations 76A20: Thin fluid films


Liu, Changchun. A sixth-order thin film equation in two space dimensions. Adv. Differential Equations 20 (2015), no. 5/6, 557--580.

Export citation