The curve shortening problem under Robin boundary condition. (English) Zbl 1243.53107
Summary: The curve shortening problem for a graph under Robin boundary conditions is studied in this paper. The large time behavior of the global solution is shown to depend critically on the parameters in the boundary condition. The asymptotic behavior of the solution is also discussed.
MSC:
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35B50 | Maximum principles in context of PDEs |
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