论文标题
本征函数在局部周期性振荡边界的薄域中定位
Localization of eigenfunctions in a thin domain with locally periodic oscillating boundary
论文作者
论文摘要
我们研究了二阶椭圆运算符，在薄域中具有局部周期性系数的二阶光谱问题。假定域的边界是局部周期性的。当域的厚度$ \ varepsilon $趋于零时，特征值是$ \ varepsilon^{ - 2} $的订单，并用第一个特征值$μ（x_1）$的辅助光谱细胞问题$ x_1 $ x_1 $ conterize cormine contersize cormine eigenfunctions varysize cormine the eigenvalue $μ（x_1）$进行了描述。 $ \ sqrt {\ varepsilon} $。
We study a Dirichlet spectral problem for a second-order elliptic operator with locally periodic coefficients in a thin domain. The boundary of the domain is assumed to be locally periodic. When the thickness of the domain $\varepsilon$ tends to zero, the eigenvalues are of order $\varepsilon^{-2}$ and described in terms of the first eigenvalue $μ(x_1)$ of an auxiliary spectral cell problem parametrized by $x_1$, while the eigenfunctions localize with rate $\sqrt{\varepsilon}$.
