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.
“…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
It is shown that every positive, stable H 2 0 -solution to Δu+f (u) = c in R 2 is radially symmetric. This problem arises from the study of the steady states for the two dimensional thin film equation.
“…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
It is shown that every positive, stable H 2 0 -solution to Δu+f (u) = c in R 2 is radially symmetric. This problem arises from the study of the steady states for the two dimensional thin film equation.
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