Existence and behavior of asymmetric traveling wave solutions to thin film equation

TL;DR

This paper proves the existence and uniqueness of asymmetric traveling wave solutions to the thin film equation with slip conditions, providing bounds and error estimates for these solutions.

Contribution

It establishes the existence, uniqueness, and bounds of asymmetric traveling wave solutions for the thin film equation with slip boundary conditions.

Findings

Existence and uniqueness of traveling wave solutions.

Explicit bounds for the solutions.

Error estimates for approximation accuracy.

Abstract

We proved the existence and uniqueness of a traveling wave solution to the thin film equation with a Navier slip condition at the liquid-solid interface. We obtain explicit lower and upper bounds for the solution and an absolute error estimate of approximation of a solution to the thin films equation by the traveling-wave solution.