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Dichotomy of Linear Partial Differential Equations of Neutral Type in Banach Spaces
Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2020-06-29 , DOI: 10.1007/s10884-020-09864-1
Marieme Lasri , Hamid Bounit , Said Hadd

This present paper is mainly devoted to investigate the property of spectral decomposition of neutral differential equations in infinite dimensional setting, that is the exponential dichotomy. In fact, we prove that the exponential dichotomy of the associated semigroup to such equations does not depend on that of their associated difference equations. Based on the regular linear systems and feedback theory, we introduce a new transformation of neutral-type equations which plays a key role in our investigation.



中文翻译:

Banach空间中立型线性偏微分方程的二分法。

本文主要致力于研究中立型微分方程在无穷维情况下的频谱分解特性,即指数二分法。实际上,我们证明了相关半群与此类方程的指数二分法并不取决于其相关差分方程的指数二分法。在常规线性系统和反馈理论的基础上,我们介绍了一种中立型方程的新变换,它在我们的研究中起着关键作用。

更新日期:2020-06-29
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