TY - JOUR

T1 - Compact traveling waves for anisotropic curvature flows with driving force

AU - Monobe, H.

AU - Ninomiya, H.

N1 - Publisher Copyright:
© 2021 American Mathematical Society.

PY - 2021/4

Y1 - 2021/4

N2 - To study the dynamics of an anisotropic curvature flow with external driving force depending only on the normal vector, we focus on traveling waves composed of Jordan curves in R2. Here we call them compact traveling waves. The objective of this study is to investigate thoroughly the condition of the driving force for the existence of compact traveling waves to the anisotropic curvature flow. It is shown that all traveling waves are strictly convex and unstable, and that a compact traveling wave is unique, if they exist. To determine the existence of compact traveling waves, three cases are considered: if the driving force is positive, there exists a compact traveling wave; if it is negative, there is no traveling wave; if it is sign-changing, a positive answer is obtained under the assumption called “admissible condition”. We also obtain a necessary and sufficient condition for the existence of axisymmetric compact traveling waves. Lastly, we make reference to the inverse problem and non-convex compact traveling waves.

AB - To study the dynamics of an anisotropic curvature flow with external driving force depending only on the normal vector, we focus on traveling waves composed of Jordan curves in R2. Here we call them compact traveling waves. The objective of this study is to investigate thoroughly the condition of the driving force for the existence of compact traveling waves to the anisotropic curvature flow. It is shown that all traveling waves are strictly convex and unstable, and that a compact traveling wave is unique, if they exist. To determine the existence of compact traveling waves, three cases are considered: if the driving force is positive, there exists a compact traveling wave; if it is negative, there is no traveling wave; if it is sign-changing, a positive answer is obtained under the assumption called “admissible condition”. We also obtain a necessary and sufficient condition for the existence of axisymmetric compact traveling waves. Lastly, we make reference to the inverse problem and non-convex compact traveling waves.

KW - Algebraic geometry

KW - Differential geometry

UR - http://www.scopus.com/inward/record.url?scp=85102125133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85102125133&partnerID=8YFLogxK

U2 - 10.1090/tran/8168

DO - 10.1090/tran/8168

M3 - Article

AN - SCOPUS:85102125133

SN - 0002-9947

VL - 374

SP - 2447

EP - 2477

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 4

ER -