求解小周期系数的混合边值问题Schwarz交替法与双尺度渐近分析法的耦合

THE METHOD COUPLING SCHWARZ ALTERNATE AND TWO-SCALE ANALYSIS METHOD FOR SOLVING MIXED PROBLEMS WITH SMALL PERIODIC COEFFICIENTS

本文我们讨论了具有周期孔隙区域上弹性系统的混合边值问题，其中外部边界是位移和力的混合边界，孔隙表面是Dirichlet位移边界条件．目前还没有人得到这一问题的双尺度完全渐近展开式，主要困难在于余法线项在边界Ω附近难以估计．我们借助Schwarz交替法的思想，得到该问题的双尺度渐近分析结果．

In present paper, we consider the mixed problems in a perforated domain withthe mixed boundary condition on the outer part of the boundary and Dirichlet conditions onthe surface of the cavities. In this case some difficulties arise in estimating for the boundaryvalues of the conormal derivative outside a neighbourhood ofΩ, so far, none obtain thecompletely two-scale asymptotic expansion about this matter. By virtue of the principleidea of Schwarz alternating method, a new theoretical result is presented in this paper.