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.

引用

页码：4350 / 4385

页数：36

共 42 条

[1] TRANSLATING SURFACES OF THE NONPARAMETRIC MEAN-CURVATURE FLOW WITH PRESCRIBED CONTACT-ANGLE [J].