论文标题
方程式建模樟脑运动的短期近似解决方案
Short-time approximate solutions of an equation modeling a camphor motion
论文作者
论文摘要
作为自发运动的深刻例子，我们分析了樟脑粒子在水面上的运动。该运动被建模为在二维域中扩散方程的耦合非线性系统的初始符合物值问题。由于似乎缺少这个初始边界价值问题的良好性，我们提供了证明。然后，通过构建对这个初始边界价值问题的近似解决方案，我们对樟脑运动进行了数学上严格的解释。也就是说，我们表明，及时樟脑的运动具有自我避免的轨道。我们还给出了近似解决方案的数值性能。
As a profound example of spontaneous motion, we analyze the motion of a camphor particle on a water surface. The motion is modeled as an initial-boundary value problem for a coupled nonlinear system of a diffusion equation and an ordinary differential equation in a two-dimensional domain. Since it seems that the well-posedness of this initial boundary value problem is missing, we provided its proof. Then, by constructing an approximate solution to this initial boundary value problem, we gave a mathematically rigorous interpretation of a camphor motion. That is we showed that the motion of camphor locally in time has a self-avoiding orbit. We also gave the numerical performance of the approximate solution.
