Local Bifurcation-Branching Analysis of Global and "Blow-up" Patterns for a Fourth-Order Thin Film Equation

2010/09/29 by P. Álvarez-Caudevilla, Álvarez-Caudevilla, P., V. A. Galaktionov +1
Mathematics · #35 K 55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35 #msc:55

paper · pdf · doi:10.48550/arxiv.1009.5864

48 pages, 1 figure

arxiv created 2010/09/29 · arxiv updated 2010/09/30

Abstract

The quasilinear fourth-order thin film equation in R^N is shown to admit infinite countable families of global and blow-up similarity solutions, which are originated in the limit from eigenfunctions of the corresponding linear non-self-adjoint operators.

Related

• Branching analysis of a countable family of global similarity solutions of a fourth-order thin film equation
• On Continuous Branches of Very Singular Similarity Solutions of the Stable Thin Film Equation
• On Oscillations of Solutions of the Fourth-Order Thin Film Equation Near Heteroclinic Bifurcation Point
• Self-similar lifting and persistent touch-down points in the thin-film equation
• Three tupes of self-similar blow-up for the fourth-order p-Laplacian equaiton with source: variational and branching approaches