静电力驱动的肥皂膜桥的动力学行为
Dynamical Behaviour of a Soap Film Bridge Driven by an Electrostatic Force
AI总结：
本文研究静电力驱动下管状肥皂膜桥的自由边界问题，通过将旋转对称情形改写为带非局部源项的拟线性抛物方程证明局部适定性，并证明大电压下解不能全局存在。
摘要：
我们研究一个描述由静电力驱动的管状肥皂膜桥的自由边界问题。为了实现静电力，肥皂膜桥被放置在一个外部金属圆柱体内，并在该圆柱体与肥皂膜之间施加电压差。我们的模型由一个描述薄膜演化的拟线性抛物方程和一个描述外部圆柱体与肥皂膜桥之间未知区域内静电势的椭圆方程耦合而成。对于旋转对称情形，我们通过将该自由边界问题改写为一个带非局部源项的单一拟线性抛物方程，证明了其局部适定性。此外，对于较大的施加电压，我们证明对于一大类初始值，解不能全局存在。
英文摘要：
We study a free boundary problem describing a tubular soap film bridge driven by an electrostatic force. To realize the electrostatic force, the soap film bridge is placed inside an outer metal cylinder and a voltage difference between this cylinder and the soap film is applied. Our model consists of a quasilinear parabolic equation for the evolution of the film coupled with an elliptic equation for the electrostatic potential in the unknown domain between outer cylinder and soap film bridge. For the rotationally symmetric case, we prove local well-posedness of this free boundary problem by recasting it as a single quasilinear parabolic equation with a non-local source term. Moreover, for large applied voltages, we show that solutions do not exist globally for a wide class of initial values.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
