标题： 有界剖面中垂直入渗的解析解 显示英文标题

标题： An analytical solution for vertical infiltration in bounded profiles

摘要： 在本研究中，我们推导出一个解析解，以解决有限剖面内一维垂直入渗的问题。 我们考虑 Richards 方程以及各种边界条件，模拟水在均质且有限介质表面的不同应用情景。 为了解有限区间上的相应初始边界值问题，我们应用了统一变换，通常称为 Fokas 方法。 通过这种方法，我们得到一个可以高效直接进行数值计算的积分表达式，从而得到一个收敛的方案。 显示英文摘要

摘要： In this study, we derive an analytical solution to address the problem of one-dimensional vertical infiltration within bounded profiles. We consider the Richards equation together with various boundary conditions, simulating different scenarios of water application onto the surface of a homogeneous and bounded medium. To solve the corresponding initial boundary value problem over a finite interval, we apply the unified transform, commonly known as the Fokas method. Through this methodology, we obtain an integral representation that can be efficiently and directly computed numerically, yielding a convergent scheme.