2012
DOI: 10.1088/0951-7715/25/12/3343
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A mountain pass scenario and heteroclinic orbits for thin-film type equations

Abstract: General results on the existence of mountain pass scenarios and heteroclinic orbits for the steady states of the thin-film type equations are present. Applied to the special case f (h) = h q , they provide analytic justifications to some known numerical results. The dynamics of the thin film for q ∈ (1, 3) is described in detail.

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Cited by 4 publications
(1 citation statement)
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“…As seen from linearization, the constant states will lose their stability in the so-called long wave situation. The classification and stability of the steady states for the 1-D thin film equation have been studied in [18]- [21], [9], [11]. The notion of energy stability has turned out to be useful in these studies.…”
Section: Droplets Of the Thin Film Equationmentioning
confidence: 99%
“…As seen from linearization, the constant states will lose their stability in the so-called long wave situation. The classification and stability of the steady states for the 1-D thin film equation have been studied in [18]- [21], [9], [11]. The notion of energy stability has turned out to be useful in these studies.…”
Section: Droplets Of the Thin Film Equationmentioning
confidence: 99%