Geometric flows for elastic functionals of curves and the applications

Geometric flows for elastic functionals of curves and the applications

Tran The Dung(Tran The Dung)

指導教授 ： 林俊吉

國立臺灣師範大學/理學院/數學系/博士(2022年)

https://doi.org/10.6345/NTNU202200953

摘要

None

關鍵字

None

並列摘要

In this thesis, the method of geometric flow is applied to prove the existence of global solutions to the problem of nonlinear spline interpolations for closed/non-closed curves and the problem of area-constrained planar elasticae with free boundaries on a straight line. Among them, this method applies the theory of either fourth-order parabolic PDEs/PDE or second-order parabolic PDEs/PDE with certain imposed boundary conditions. The results of this study demonstrate the existence of global solutions and sub-convergence of the elastic flow. Furthermore, the geometric flow method provides a new approach to the problem of nonlinear spline interpolations.

並列關鍵字

Geometric flow ； elastic flow ； fourth-order parabolic equation ； second-order parabolic equation ； elastic spline ； spline interpolation ； curve fitting ； path planning ； free boundary problem ； contact angles ； Holder spaces

參考文獻

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