Liquid drops sliding down an inclined plane

2012/03/13 by Inwon Kim, Kim, Inwon, Antoine Mellet +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.AP

paper · pdf · doi:10.48550/arxiv.1203.2942

33 pages, 2 figures

arxiv created 2012/03/13 · openalex publication_date 2012/03/13 · arxiv updated 2012/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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