Abstract
We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial differential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature flow equation and apply to more general Neumann-type boundary problems for parabolic equations in the level set approach to motion of hypersurfaces with velocity depending on the normal direction and curvature.
| Original language | English |
|---|---|
| Pages (from-to) | 1077-1098 |
| Number of pages | 22 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 57 |
| Issue number | 7-8 |
| DOIs | |
| Publication status | Published - 2004 Jun |
Keywords
- Capillary problem
- Mean curvature flow
- Neumann-type boundary conditions
- Singular degenerate parabolic equations
- Viscosity solutions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Mathematics(all)
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Ishii, H., & Sato, M. H. (2004). Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. Nonlinear Analysis, Theory, Methods and Applications, 57(7-8), 1077-1098. https://doi.org/10.1016/j.na.2004.04.003