One-Dimensional Parabolic Free Boundary Problems
One-Dimensional Parabolic Free Boundary Problems
复制标题
一维抛物线自由边界问题
DOI：
--
复制
发表时间：
1977
期刊：
影响因子：
--
通讯作者：
G. Meyer
中科院分区：
文献类型：
--
作者：
G. Meyer
通常，扩散过程需要根据过度规定的边界数据确定自由面。解决这类问题的一种常用的构造性方法是直线法。本文对解决过程中涉及的步骤进行了说明。具体地说，用直线法逼近一维线性扩散方程的各种显式和隐式自由边值问题以及一系列的常微分方程组的自由边值问题。结果表明，这些方程具有用不变嵌入方法很容易得到的解。对于一个模型问题，当离散化参数趋于零时，近似解收敛到唯一的(几乎)经典解。
Frequently, diffusion processes require the determination of a free surface from overprescribed boundary data. A commonly used constructive solution technique for such problems is the method of straight lines. This paper illustrates the steps involved in the solution process. Specifically, the method of lines is used to approximate various explicit and implicit free boundary problems for a linear one-dimensional diffusion equation with a sequence of free boundary problems for ordinary differential equations. It is shown that these equations have solutions which can be readily obtained with the method of invariant imbedding. It also is established for a model problem that the approximate solutions converge to a unique (almost) classical solution as the discretization parameter goes to zero.