On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane
On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane
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平面裂纹外部拉普拉斯方程的修正跳跃问题
DOI：
10.1155/2012/579457
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发表时间：
2012
影响因子：
1.2
通讯作者：
A.
中科院分区：
文献类型：
--
作者：
Krutitskii;PA and Sasamoto;A.
研究了平面内多个裂纹外部拉普拉斯方程的边值问题。在裂纹上指定拉普拉斯方程解的跳跃和包含其法导数跳跃的边界条件。该问题在一定条件下有唯一的经典解。获得了该问题唯一解的新积分表示。该问题被简化为唯一可解的第二类 Fredholm 方程且下标为零。积分表示和积分方程本质上比之前针对该问题导出的更简单。研究了裂纹末端的奇点。
The boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under certain conditions. The new integral representation for the unique solution of this problem is obtained. The problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero. The integral representation and integral equation are essentially simpler than those derived for this problem earlier. The singularities at the ends of the cracks are investigated.