Systems with strong damping and their spectra
Systems with strong damping and their spectra
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DOI：
10.1002/mma.5166
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发表时间：
2018-11-15
影响因子：
2.9
通讯作者：
Vogt, Hendrik
中科院分区：
文献类型：
--
作者：
Jacob, Birgit;Tretter, Christiane;Vogt, Hendrik
本文建立了一种新的方法，用于在Hilbert空间中获得与二阶微分方程zd=0相关的算子的非凸谱包络。特别是，我们成功地建立了一个频谱间隙的存在，这是第一个这样的结果，因为开创性的结果Krein和Langer阻尼系统的振荡。虽然后者和其他谱边界仅限于对称且由A（0）支配的阻尼D，但我们允许与A（0）强度相等的增生D。为了实现这些结果，我们证明了新的抽象谱包含结果，比经典的数值范围界限更强大。两个不同的应用程序，小横向振荡的水平管道进行稳态流的理想不可压缩流体和波动方程具有强（粘弹性和摩擦）阻尼，说明我们的新的边界是明确的。
We establish a new method for obtaining nonconvex spectral enclosures for operators associated with second-order differential equations zd=0 in a Hilbert space. In particular, we succeed in establishing the existence of a spectral gap, which is the first result of this kind since the seminal results of Krein and Langer for oscillations of damped systems. While the latter and other spectral bounds are confined to dampingsD that are symmetric and dominated by A(0), we allow for accretive D of equal strength as A(0). To achieve these results, we prove new abstract spectral inclusion results that are much more powerful than classical numerical range bounds. Two different applications, small transverse oscillations of a horizontal pipe carrying a steady-state flow of an ideal incompressible fluid and wave equations with strong (viscoelastic and frictional) damping, illustrate that our new bounds are explicit.