Existence of Non-convex Traveling Waves for Surface Diffusion of Curves with Constant Contact Angles

Takashi Kagaya, Yoshihito Kohsaka

Research output: Contribution to journalArticle

Abstract

The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane curve governed by surface diffusion, we discuss the existence, the uniqueness and the convexity of traveling waves. The main results show that the uniqueness and the convexity can be lost depending on the conditions of the contact angles, although the existence holds for any contact angles in the interval (0 , π/ 2).

Original languageEnglish
JournalArchive for Rational Mechanics and Analysis
DOIs
Publication statusPublished - Jan 1 2019

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Surface Diffusion
Surface diffusion
Contact Angle
Plane Curve
Traveling Wave
Contact angle
Curve
Convexity
Uniqueness
Interval

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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abstract = "The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane curve governed by surface diffusion, we discuss the existence, the uniqueness and the convexity of traveling waves. The main results show that the uniqueness and the convexity can be lost depending on the conditions of the contact angles, although the existence holds for any contact angles in the interval (0 , π/ 2).",
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