On centre subspace behaviour in thin flm equations

Abstract

It is shown that the fourth-order parabolic thin film equation with critical absorption admits the large time behaviour, where special logarithmic perturbations enter the standard source-type asymptotics. Such asymptpotic phenomena on existence of logarithmic factors are known for semilinear heat equation with absorption since the 1980s.

27 pages, 4 figures

Cited by in corpus (4)

• On Oscillations of Solutions of the Fourth-Order Thin Film Equation Near Heteroclinic Bifurcation Point
• Very singular solutions for the thin film equation with absorption
• On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation I. Local oscillatory properties
• On Continuous Branches of Very Singular Similarity Solutions of the Stable Thin Film Equation