AI Article Synopsis
- The research focuses on how fixed-length curves, subject to clamped boundary conditions, evolve over time by following the negative gradient flow of their elastic energy.
- It establishes the existence of a solution for initial curves within a specific energy space and demonstrates that these solutions become smoother as time progresses.
- By using prior findings on long-term existence and proving a specialized gradient inequality, the study concludes that these curves converge to a critical point as time approaches infinity.
Article Abstract
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative -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.
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Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11219461 | PMC |
| http://dx.doi.org/10.1007/s00028-024-00988-1 | DOI Listing |
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