具有频繁交换边界条件的三维边值问题的渐近性和收敛度估计
Asymptotics and Estimates of Degrees of Convergence in Three-Dimensional Boundary Value Problem with Frequent Interchange of Boundary Conditions
摘要：
考虑侧面边界条件类型频繁互换的圆柱体中拉普拉斯算子的奇异扰动本征值问题。这些边界条件是在狄利克雷条件和诺依曼条件交替施加的基础上，通过将侧表面划分成大量的窄条来规定的。本文研究了在侧表面上含有Dirichlet条件的齐次化问题的情形。当条带宽度缓慢变化时，我们构造了特征元渐近展开式的主导项。我们还估计了当带的宽度迅速变化时特征值的收敛程度。
英文摘要：
We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in a great number of narrow strips on those the Dirichlet and Neumann conditions are imposed by turns. We study the case of the homogenized problem containing Dirichlet condition on the lateral surface. When the width of strips varies slowly, we construct the leading terms of eigenelements' asymptotics expansions. We also estimate the degree of convergence for eigenvalues if the strips' width varies rapidly.
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