Advances in Differential Equations

A sixth-order thin film equation in two space dimensions

Changchun Liu

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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.

Article information

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

Dates
First available in Project Euclid: 30 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1427744016

Mathematical Reviews number (MathSciNet)
MR3327707

Zentralblatt MATH identifier
1319.35101

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

Citation

Liu, Changchun. A sixth-order thin film equation in two space dimensions. Adv. Differential Equations 20 (2015), no. 5/6, 557--580. https://projecteuclid.org/euclid.ade/1427744016.


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