Liquid drops sliding down an inclined plane
Inwon Kim, Antoine Mellet

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.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Geometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals
