On Oscillations of Solutions of the Fourth-Order Thin Film Equation Near Heteroclinic Bifurcation Point

Abstract

It is shown that solutions of the Cauchy for the fourth-order thin film equation becomes non-oscillatory and non-sign-changing precisely at and above the heteroclinic bifurcation point n=1.75987..., so that, possibly, these solutions begin to coincide with nonnegative solutions of a standard and well-known free-boundary problem.

15 pages, 11 Figures

References in corpus (1)

• On centre subspace behaviour in thin flm equations

Cited by in corpus (1)

• Sharp Interface Limits of the Cahn-Hilliard Equation with Degenerate Mobility