Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle. (English) Zbl 0812.35063

The authors study the mean curvature flow of two dimensional graphs over convex domains in \(\mathbb{R}^ 2\) with prescribed contact angle at the boundary. Under some reasonable assumptions they show that such a graph remains smooth and converges as \(t\to\infty\) to a unique graph moving by translation at constant speed. This generalizes an earlier work of the authors [Math. Ann. 295, No. 4, 761-765 (1993; Zbl 0798.35063)] on the one dimensional case, and of G. Huisken [J. Differ. Equations 77, No. 2, 369-378 (1989; Zbl 0686.34013)], who proved an analogous result in any dimension for the special case of vertical contact angle.
Reviewer: J.Urbas (Canberra)


35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K55 Nonlinear parabolic equations
58J35 Heat and other parabolic equation methods for PDEs on manifolds
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