Chen, Yun-Gang; Giga, Yoshikazu; Goto, Shun’ichi Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. (English) Zbl 0696.35087 J. Differ. Geom. 33, No. 3, 749-786 (1991). A weak formulation is introduced for motions of a hypersurface including the motion by mean curvature so that one tracks its evolution even after the time when there appear singularities. A unique global weak solution is constructed for an arbitrary intial hypersurface to various motions including motion by mean curvature and its anisotropic version. The hypersurface is regarded as a level set of a function solving a singular degenerate parabolic equation with special invariance called geometric. The theory of viscosity solutions is extended to our singular equations. Reviewer: Y.Giga Cited in 6 ReviewsCited in 251 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35D05 Existence of generalized solutions of PDE (MSC2000) 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:viscosity solutions PDF BibTeX XML Cite \textit{Y.-G. Chen} et al., J. Differ. Geom. 33, No. 3, 749--786 (1991; Zbl 0696.35087) Full Text: DOI