Asymptotic Dynamics of Forced Curvature Flow in a Planar Strip with Robin Boundary Conditions

@misc{pu2026asymptotic,
  title = {{Asymptotic Dynamics of Forced Curvature Flow in a Planar Strip with Robin Boundary Conditions}},
  author = {Tianhong Pu and Xiaoqian Xin and Lixia Yuan and Xiaoyu Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08270},
  eprint = {2610.08270},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08270},
}

TY  - UNPB
TI  - Asymptotic Dynamics of Forced Curvature Flow in a Planar Strip with Robin Boundary Conditions
AU  - Tianhong Pu
AU  - Xiaoqian Xin
AU  - Lixia Yuan
AU  - Xiaoyu Zhang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08270
UR  - https://arxiv.org/abs/2610.08270
AB  - We study the graphical forced mean curvature flow in a planar strip subject to Robin boundary conditions. The normal velocity is prescribed by V=H+b, where b>0 is constant and H denotes the curvature of the graph. We consider positive even solutions and reduce the problem to the half interval. The main results describe the degeneration produced by the Robin condition: the height, the instantaneous velocity, and the spatial gradient diverge, while the normalized slope u_x/u converges to one away from the symmetry axis. The normalized velocity u_t/u converges to the forcing parameter b. The curvature converges to zero in the interior in an integral sense, whereas its horizontal curvature measure concentrates at the symmetry axis.
ER  -