一类Poisson问题的近似传递条件
Approximate transmission conditions for a Poisson problem at mid-diffusion
摘要：
本文研究了$\mathbb{R}^{P}$ $(P=2,3)$的有界薄层区域中泊松方程解的渐近分析。我们使用一种基于分层变分方程的方法来推导解关于薄层厚度的渐近展开。我们确定的前三项的扩展和证明的误差估计截断后的有限数量的条款的扩展。接下来，使用前两项的渐近展开，我们表明，我们可以模拟的薄层的效果与传输条件的二阶的问题。
英文摘要：
This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of $\mathbb{R}^{P}$ $(P=2,3)$ with a thin layer. We use a method based on hierarchical variational equations to derive asymptotic expansion of the solution with respect to the thickness of the thin layer. We determine the first three terms of the expansion and prove the error estimate made by truncating the expansion after a finite number of terms. Next, using the first two terms of the asymptotic expansion, we show that we can model the effect of the thin layer by a problem with transmission conditions of order two.
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