论文标题
非组织周期方程的高频均质化
High-frequency homogenization of nonstationary periodic equations
论文作者
论文摘要
我们考虑一个椭圆形的差异操作员$ a_ \ varepsilon = - \ frac {d} {dx} g（x/\ varepsilon）\ frac {d} {dx} {dx} + \ varepsilon^{-2} $ L_2（\ Mathbb {r}）$。对于具有Hamiltonian $ a_ \ varepsilon $的非组织schrödinger方程，以及与操作员$ a_ \ a_ \ varepsilon $的双曲方程，同质化问题的类似物，与运算符$ a_ \ varepsilon $的光谱频段相关的均质边缘（称为himegendized），称为sighentization high sighentization（所谓的sighentization）。对于具有特殊初始数据的这些方程式的Cauchy问题的解决方案，获得了$ L_2（\ Mathbb {r}）$ - 小$ \ Varepsilon $的近似值。
We consider an elliptic differential operator $A_\varepsilon = - \frac{d}{dx} g(x/\varepsilon) \frac{d}{dx} + \varepsilon^{-2} V(x/\varepsilon)$, $\varepsilon > 0$, with periodic coefficients acting in $L_2(\mathbb{R})$. For the nonstationary Schrödinger equation with the Hamiltonian $A_\varepsilon$ and for the hyperbolic equation with the operator $A_\varepsilon$, analogs of homogenization problems, related to the edges of the spectral bands of the operator $A_\varepsilon$, are studied (the so called high-frequency homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in $L_2(\mathbb{R})$-norm for small $\varepsilon$ are obtained.
