Liquid drops sliding down an inclined plane

TL;DR

This paper studies a mathematical model of liquid drops sliding down an inclined plane, proving existence, uniqueness, and analyzing long-term behavior and homogenization effects in different media.

Contribution

It introduces a rigorous analysis of a one-dimensional quasi-static model, including existence, uniqueness, and long-term behavior of solutions, with homogenization results for varying media.

Findings

Proved existence and uniqueness of solutions.

Analyzed long-term behavior of the model.

Obtained homogenization results for inhomogeneous media.

Abstract

We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time behavior for both homogeneous and inhomogeneous medium (i.e. constant and non-constant contact angle). We also obtain some homogenization results.