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.
Highlights
We investigate the sixth-order thin film equation
The equation (1.1) is a typical higher order equation, which has a sharp physical background and a rich theoretical connotation. It arises in the industrial application of the isolation oxidation of silicon [8, 10]
We introduce the weak solutions in the following sense
Summary
The equation (1.1) is a typical higher order equation, which has a sharp physical background and a rich theoretical connotation. It arises in the industrial application of the isolation oxidation of silicon [8, 10]. Bernis and Friedman [5] have studied the initial boundary value problems to the thin film equation. = 0, where f (u) = |u|nf0(u), f0(u) > 0, n ≥ 1 and proved the existence of weak solutions preserving nonnegativity. Evans, Galaktionov and King [8, 9] considered the sixth-order thin film equation containing an unstable (backward parabolic) second-order term.
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