Branching analysis of a countable family of global similarity solutions of a fourth-order thin film equation

TL;DR

This paper investigates the asymptotic behavior of solutions to a fourth-order thin film equation, revealing how they branch from solutions of the linear bi-harmonic equation, including a countable set of self-similar solutions.

Contribution

It introduces a novel branching analysis connecting nonlinear thin film solutions to linear bi-harmonic solutions, expanding understanding of their asymptotic properties.

Findings

Identification of a countable family of self-similar solutions.

Demonstration of branching from linear bi-harmonic solutions.

Insights into the asymptotic properties of global solutions.

Abstract

We show that various asymptotic properties of global solutions of a fourth-order quasilinear thin film equation can be described by branching from corresponding solutions of the linear bi-harmonic equation. This includes a countable family of self-similar solutions and other aspects.