ASYMPTOTIC EXPANSIONS OF EIGENFUNCTIONS AND EIGENVALUES OF THE STEKLOV SPECTRAL PROBLEM IN THIN PERFORATED DOMAINS WITH RAPIDLY VARYING THICKNESS AND DIFFERENT LIMIT DIMENSIONS

A. V. Popov

首页> 外文期刊>Journal of Mathematical Sciences >ASYMPTOTIC EXPANSIONS OF EIGENFUNCTIONS AND EIGENVALUES OF THE STEKLOV SPECTRAL PROBLEM IN THIN PERFORATED DOMAINS WITH RAPIDLY VARYING THICKNESS AND DIFFERENT LIMIT DIMENSIONS

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ASYMPTOTIC EXPANSIONS OF EIGENFUNCTIONS AND EIGENVALUES OF THE STEKLOV SPECTRAL PROBLEM IN THIN PERFORATED DOMAINS WITH RAPIDLY VARYING THICKNESS AND DIFFERENT LIMIT DIMENSIONS

机译：具有快速变化的厚度和不同极限尺寸的薄穿孔区域中斯蒂夫洛夫谱问题的特征函数和特征值的渐近展开

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We consider a Steklov spectral problem for an elliptic differential equation with rapidly oscillating coefficients for thin perforated domains with rapidly varying thickness. We describe asymptotic algorithms for the solution of problems of this kind for thin perforated domains with different limit dimensions. We also establish asymptotic estimates for eigenvalues of the Steklov spectral problem for thin perforated domains with different limit dimensions. For certain symmetry conditions imposed on the structure of thin perforated domain and on the coefficients of differential operators, we construct and substantiate asymptotic expansions for eigenfunctions and eigenvalues.

机译：我们考虑椭圆型微分方程的Steklov谱问题，该椭圆型微分方程的厚度快速变化的薄穿孔区域具有快速振荡系数。我们描述了渐近算法，用于解决具有不同极限尺寸的薄穿孔区域的这类问题。我们还为具有不同极限尺寸的薄穿孔区域的Steklov谱问题的特征值建立了渐近估计。对于施加在薄穿孔域结构和微分算子系数上的某些对称条件，我们构造并证实了本征函数和本征值的渐近展开。

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《Journal of Mathematical Sciences》 |2017年第3期|311-336|共26页
作者
A. V. Popov;
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Shevchenko Kyiv National University, Volodymyrs'ka Str., 64/13, Kyiv, 01601, Ukraine;

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ASYMPTOTIC EXPANSIONS OF EIGENFUNCTIONS AND EIGENVALUES OF THE STEKLOV SPECTRAL PROBLEM IN THIN PERFORATED DOMAINS WITH RAPIDLY VARYING THICKNESS AND DIFFERENT LIMIT DIMENSIONS

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