论文标题
空间相互作用曲线家族的运动的定性和数值方面
Qualitative and numerical aspects of a motion of a family of interacting curves in space
论文作者
论文摘要
在本文中，我们研究了一个几何进化方程系统，描述了正常和双向方向上3D曲线家族的曲率驱动运动。不断发展的曲线可能是具有局部或非局部特征的相互作用的主题，其中整个曲线可能影响其他曲线的演变。这种演变和相互作用可以在应用中找到。我们探索了处理这种相互作用曲线的几何流量的直接拉格朗日方法。使用非线性分析半流的抽象理论，我们能够证明经典的Hölder平滑解决方案对非线性抛物线方程的管理系统的局部存在，独特性和延续。使用有限体积方法，我们构建了一个有效的数值方案解决非线性抛物线方程的管理系统。此外，考虑到非平凡的切向速度，允许对离散节点进行重新分布。我们还介绍了几项计算研究，该研究结合了正常和二维速度以及考虑非局部相互作用的流动。
In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of 3D curves in the normal and binormal directions. Evolving curves may be subject of mutual interactions having both local or nonlocal character where the entire curve may influence evolution of other curves. Such an evolution and interaction can be found in applications. 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 nonlinear parabolic equations. Using the finite volume method, we construct an efficient numerical scheme solving the governing system of nonlinear parabolic equations. Additionally, a nontrivial tangential velocity is considered allowing for redistribution of discretization nodes. We also present several computational studies of the flow combining the normal and binormal velocity and considering nonlocal interactions.
