Abstract
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative L2-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Łojasiewicz–Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.
Original language | English |
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Article number | 59 |
Journal | Journal of Evolution Equations |
Volume | 24 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2024 |
Austrian Fields of Science 2012
- 101002 Analysis
- 101006 Differential geometry
- 101028 Mathematical modelling
- 101027 Dynamical systems
Keywords
- 35K55
- Clamped boundary conditions
- Elastic energy
- Nonlocal geometric evolution equation
- Primary 53E40
- Secondary 35K52
- Willmore functional
- Łojasiewicz–Simon gradient inequality