TY - JOUR
T1 - Existence of Non-convex Traveling Waves for Surface Diffusion of Curves with Constant Contact Angles
AU - Kagaya, Takashi
AU - Kohsaka, Yoshihito
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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).
AB - 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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U2 - 10.1007/s00205-019-01426-0
DO - 10.1007/s00205-019-01426-0
M3 - Article
AN - SCOPUS:85068977348
VL - 235
SP - 471
EP - 516
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 1
ER -