2024/05/02 by Miroslav Kolář, Kolar, Miroslav, Daniel Ševčovič +1 · 1 citation
Computer Science · Engineering · #35K65 #3D Shape Modeling and Analysis #65M08 #65N40 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA) #Primary: 35K57 #Secondary: 53C80
paper · pdf · doi:10.48550/arxiv.2405.01038
openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate a system of geometric evolution equations describing a curvature and torsion driven motion of a family of 3D curves in the normal and binormal directions. We explore the direct Lagrangian approach for treating the geometric flow of such interacting curves. Using the abstract theory of nonlinear analytic semi-flows, we are able to prove local existence, uniqueness, and continuation of classical Hölder smooth solutions to the governing system of non-linear parabolic equations modelling n evolving curves with mutual nonlocal interactions. We present several computational studies of the flow that combine the normal or binormal velocity and considering nonlocal interaction.