论文标题
沿给定的歧管与非线性罗宾条件在腔边界的给定歧管的穿孔问题的标准收敛
Norm convergence for problems with perforation along a given manifold with nonlinear Robin condition on boundaries of cavities
论文作者
论文摘要
在工作中，我们考虑了一个二阶方程的边界值问题，其在多维域中具有可变系数的小空腔穿孔，该型号沿给定的歧管紧密间隔。我们假设所有空腔的线性尺寸均具有相同的较小顺序，而它们的形状和分布是任意的。腔的边界受到非线性罗宾条件的影响。我们证明，扰动问题的解决方案会收敛到norm $ l_2 $和$ w_2^1 $中的均质问题的解决方案，在等式中右侧的$ l_2 $ - norm中均匀。我们还建立了收敛速率的估计值。
In the work we consider a boundary value problem for a second order equation with variable coefficients in a multi-dimensional domain perforated by small cavities closely spaced along a given manifold. We assume that the linear sizes of all cavities are of a same order of smallness, while their shapes and distributions are arbitrary. The boundaries of the cavities are subject to a nonlinear Robin condition. We prove that the solution of the perturbed problem converges to that of the homogenized problem in norm $L_2$ and $W_2^1$ uniformly in $L_2$-norm of the right hand side in the equation. We also establish the estimates for the convergence rates.
