Elastic flow of networks: short-time existence result

Anna Dall’Acqua*, Chun Chi Lin, Paola Pozzi

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this paper we study the L2-gradient flow of the penalized elastic energy on networks of q-curves in Rn for q≥ 3. Each curve is fixed at one end-point and at the other is joint to the other curves at a movable q-junction. For this geometric evolution problem with natural boundary condition we show the existence of smooth solutions for a (possibly) short interval of time. Since the geometric problem is not well-posed, due to the freedom in reparametrization of curves, we consider a fourth-order non-degenerate parabolic quasilinear system, called the analytic problem, and show first a short-time existence result for this parabolic system. The proof relies on applying Solonnikov’s theory on linear parabolic systems and Banach fixed point theorem in proper Hölder spaces. Then the original geometric problem is solved by establishing the relation between the analytical solutions and the solutions to the geometrical problem.

原文英語
頁(從 - 到)1299-1344
頁數46
期刊Journal of Evolution Equations
21
發行號2
DOIs
出版狀態已發佈 - 2021 六月

ASJC Scopus subject areas

  • 數學(雜項)

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