Analysis shows smooth convergence of the elastic flow of constrained curves, indicating stability.
We investigate the asymptotic stability of the length-penalized elastic flow of curves with boundary points constrained to the x-axis in R². The main tool in our analysis is the Lojasiewicz--Simon inequality, which is used to prove that the flow smoothly converges to an elastica.
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Antonia Diana (2025) studied this question.
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