TY - JOUR
T1 - Global Existence of a Mean Curvature Flow in a Cone
AU - Ai , Neng
AU - Lou , Bendong
AU - Song , Jiashu
AU - Yang , Pei
AU - Zhang , Xin
JO - Journal of Mathematical Study
VL - 3
SP - 278
EP - 293
PY - 2024
DA - 2024/10
SN - 57
DO - http://doi.org/10.4208/jms.v57n3.24.03
UR - https://global-sci.org/intro/article_detail/jms/23489.html
KW - Mean curvature flow, quasilinear parabolic equation, free boundary problem, self-similar solution.
AB - <p style="text-align: justify;">We consider a mean curvature flow in a cone, that is, a hypersurface in a
cone which propagates toward the opening of the cone with normal velocity depending on its mean curvature. In addition, the contact angle between the hypersurface and
the cone boundary depending on its position. First, we construct a family of radially
symmetric self-similar solutions. Then we use these solutions to give a priori estimates
for the solutions of the initial boundary value problems, and show their global existence.</p>