偏微分方程的满足部分边界条件的解的多样性
The Diversity of Solutions Satisfied Partial Boundary Conditions for a Partial Differential Equation
DOI: 10.12677/AAM.2018.75073, PDF,    科研立项经费支持
作者: 李丹丹, 银 山*：内蒙古工业大学理学院，内蒙古 呼和浩特
关键词: 偏微分方程；Dirichlet边值问题；Adomian分解法；Partial Differential Equations； Dirichlet Boundary Value Problem； Adomian Decomposition Method
摘要: 对偏微分方程的(初)边值问题，目前的大多数求解方法基于其部分(初)边界条件。那么这样得到的解能否满足所有边界条件呢？为此，我们基于Adomian分解法，求解三角形地下水域上补给效应模型的Dirichlet边值问题。我们发现：1) 求出的解有时满足所有边界条件，有时不满足；2) 满足部分边界条件的解不是唯一；3) Adomian分解法得到的解是满足部分边界条件的某一个特解。
Abstract: For (initial) boundary value problems of partial differential equations, most of current methods are based on their partial (initial) boundary conditions. Then the solution obtained in this way could satisfy all the boundary conditions? For this reason, we based on Adomian decomposition method to solve the Dirichlet boundary value problem of groundwater recharge effect model on triangular area. We find that: 1) the solution satisfies all boundary conditions sometimes, sometimes not satisfies; 2) the solution satisfied partial boundary conditions is not unique; 3) the solution obtained by the Adomian decomposition method is a particular solution that satisfies partial boundary conditions.
文章引用：李丹丹, 银山. 偏微分方程的满足部分边界条件的解的多样性[J]. 应用数学进展, 2018, 7(5): 617-621. https://doi.org/10.12677/AAM.2018.75073

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