论文标题
连续培养基具有高对比度的连续培养基的操作员 - 主体分解渐近分析
Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions
论文作者
论文摘要
利用对边界值问题的分解的差距到neumann地图的经典概念以及相关公式，我们分析了在连续介质中高对比度包含解决方案对“传输问题”的渐近行为，为操作员分辨率转化为限制了“限制”功能“限制”的“范围”的“范围”。特别是，我们的结果暗示了高对比度问题的光谱与极限运算符的光谱的收敛，并具有订单 - 呈收敛的估计。
Using a generalisation of the classical notion of Dirichlet-to-Neumann map and the related formulae for the resolvents of boundary-value problems, we analyse the asymptotic behaviour of solutions to a "transmission problem" for a high-contrast inclusion in a continuous medium, for which we prove the operator-norm resolvent convergence to a limit problem of "electrostatic" type for functions that are constant on the inclusion. In particular, our results imply the convergence of the spectra of high-contrast problems to the spectrum of the limit operator, with order-sharp convergence estimates.
