Abstract
In a previous work by the authors a second order gradient flow of the p-elastic energy for a planar theta-network of three curves with fixed lengths was considered and a weak solution of the flow was constructed by means of an implicit variational scheme. Long-time existence of the evolution and convergence to a critical point of the energy were shown. The purpose of this note is to prove uniqueness of the weak solution when p = 2.
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References
Novaga, M., Pozzi, P.: A second order gradient flow of p-elastic planar networks. SIAM J. Math. Anal. 52(1), 682–708 (2020). https://doi.org/10.1137/19M1262292
Acknowledgements
MN has been supported by GNAMPA-INdAM and PP has been supported by the DFG (German Research Foundation) Projektnummer: 404870139.
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Novaga, M., Pozzi, P. (2021). Uniqueness for a Second Order Gradient Flow of Elastic Networks. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_77
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DOI: https://doi.org/10.1007/978-3-030-55874-1_77
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