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Unstable sixth-order thin film equation: I. Blow-up similarity solutions

“…In [32,33], a more general form of this equation (now allowing for a reaction at the underlying solid interface) is shown to arise in the industrial application of the isolation oxidation of silicon. Analysis for a finite length elastica or plate is given in [21], whilst a numerical scheme (in the form of a Keller-Box method) with subsequent parameter investigation of the more general system is given in [22]. A survey and a detailed analysis of interface propagation for sixth-order TFEs can be found in [24].…”

Molecular dynamics study on thermal conductance between a nanotip and a substrate under vertical forces and horizontal sliding

“…Due to ambient exposure to air, the silicon tip, like typical diamond crystals, is largely passivated by hydrogen, and hydrogen atoms will adhere thinly to the surface of the silicon tip. 2,29,37 In addition, the silicon surface is susceptible to oxidation, 38,39 and a 0.7-0.8 nm thick oxide layer 40 will exist. Other contaminants, especially water and hydrocarbons, 29 may also be present in the experiment, and these can all affect the heat transfer across the interface of the silicon tip.…”

Group properties and invariant solutions of a sixth-order thin film equation in viscous fluid

“…However, the sixth-order thin film equation ( 2) has been much less extensively investigated. It was only a few researches that were devoted to qualitative mathematic properties such as the existence of weak solutions, initial boundary value problems (see Bernis Friedman [27], King et al [28], Smith et al [29], Evans et al [30], Barrett et al [31] for existing studies, the first two being analytical and the others primarily numerical), while the symmetry group properties and corresponding algebraic structure as well as explicit exact solutions of Eq. ( 2) still remain open.…”