SINGULAR NEUMANN BOUNDARY PROBLEMS FOR A CLASS OF FULLY NONLINEAR PARABOLIC EQUATIONS IN ONE DIMENSION

被引：1
|
作者：
Kagaya, Takashi [1 ]
Liu, Qing [2 ]
机构：
[1] Kyushu Univ, Inst Math Ind, Fukuoka 8190395, Japan
[2] Fukuoka Univ, Fac Sci, Dept Appl Math, Fukuoka 8140180, Japan
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2021年 / 53卷 / 04期
关键词：
fully nonlinear parabolic equations; power mean curvature flow; viscosity solutions; large time behavior; singular Neumann problem; MEAN-CURVATURE FLOW; DEGENERATE ELLIPTIC-EQUATIONS; ALLEN-CAHN EQUATION; VISCOSITY SOLUTIONS; GENERALIZED MOTION; CONVERGENCE; EVOLUTION; GROWTH; MODEL;
D O I：
10.1137/20M1371646
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we discuss a singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes the motion of a planar curve sliding along the boundary with a zero contact angle, which can be viewed as a limiting model for the capillary phenomenon. We study the uniqueness and existence of solutions by using the viscosity solution theory. We also show the convergence of the solution to a traveling wave as time proceeds to infinity when the initial value is assumed to be convex.
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页码：4350 / 4385
页数：36
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