Integral Methods in Science and Engineering, Volume 1
Integral Methods in Science and Engineering, Volume 1
复制标题
科学与工程中的积分方法，第 1 卷
DOI：
10.1007/978-3-319-59384-5_3
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Ayele T
中科院分区：
文献类型：
--
作者：
Ayele T
本文考虑二维变系数定常热传导偏微分方程解的二阶Neumann边值问题。该方程可归结为若干个边界域积分方程组。由于偏微分方程解的存在，使得二维边界域积分方程解的构造不同于其余的维积分方程组。因此，我们需要在区域上或空间上设置条件，以确保层势的可逆性，从而确保边界域积分方程的唯一可解性。分析了BDIE与原BVPS的等价性、BDIEs的可解性、解的唯一性/非唯一性以及BDIEs算子的Fredholm性和可逆性。证明了Neumann边值问题的BDIE算子是不可逆的，并且构造了适当的有限维扰动，从而得到了扰动算子的可逆性。
In this paper we will consider second order Neumann Boundary Value problem for the “stationary heat transfer” partial differential equation with variable coefficient in two-dimension. This equation is reduced to some boundary-domain integral equations (BDIEs). The construction of Boundary-Domain Integral equation in two-dimension is special from the remaining dimension because of the associated fundamental solution to the partial differential equation. Consequently we need to set conditions on the domain or on the spaces to insure the invertibility of layer potentials and hence the unique solvability of Boundary-Domain integral equation. The equivalence of the BDIEs to the original BVPs, BDIEs solvability, solution uniqueness/nonuniqueness, as well as Fredholm property and invertibility of the BDIEs operator are analyzed. It is shown that the BDIE operators for Neumann BVP are not invertible, and appropriate finite-dimensional perturbations are constructed leading to invertibility of the perturbed operators.