圆柱面上薄膜方程收敛到平衡态
偏微分方程分析
2013-12-30 v2 数学物理
math.MP
摘要
退化抛物方程 u_t + [u^3(u_xxx + u_x - sin x)]_x=0 描述了静止水平圆柱上薄液膜的演化。本文证明，对于每个给定的质量，存在唯一的稳态，该稳态由悬挂在圆柱底部的液滴表示，液滴与顶部干燥区域以零接触角相接。该液滴使能量最小化，并吸引所有满足特定能量和熵不等式的强解。任何解到稳态的距离衰减速度不慢于幂律。
引用
@article{arxiv.1011.2108,
title = {Convergence to equilibrium for a thin film equation on a cylindrical surface},
author = {Almut Burchard and Marina Chugunova and Benjamin K. Stephens},
journal= {arXiv preprint arXiv:1011.2108},
year = {2013}
}
备注
26 pages, 6 figures. This is a greatly expanded version of our previous submission [arXiv:1009.4092v1]. The main result on convergence to equilbrium is new, and the bounds on the rate of convergence have been simplified. For the second version, we have changed the title, corrected Lemma 2.3, rewrittenSection 3, and added several references