非线性源含时滞的抽象发展方程的适定性与指数稳定性：摩擦与粘弹性情形
Well-posedness and exponential stability for abstract evolution equations with delay in the nonlinear source: frictional and viscoelastic cases
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中文总结 AI 辅助
本文针对含常数时滞的半线性中立型抽象发展方程，在摩擦与粘弹性两种阻尼下，证明了小初始数据解的全局适定性与指数稳定性，并给出统一分析框架及实例。
中文摘要 AI 辅助
本文研究一类具有常数时滞的半线性中立型抽象发展方程的适定性与指数稳定性。考虑两种阻尼机制：形如$CC^*u_t$的摩擦阻尼和带记忆的粘弹性阻尼。在适当假设下，我们证明了对于足够小的初始数据，解的全局适定性和指数衰减性。该结果具有重要意义，因为它为结构力学、隔震和控制理论中出现的广泛中立型系统分析提供了统一框架。抽象结果通过一些具体例子加以说明。分析依赖于半群理论、能量估计、Duhamel公式和Gronwall型论证的结合。
英文摘要
In this paper, we establish the well-posedness and exponential stability of a class of semilinear neutral abstract evolution equations with constant time delay. Two damping mechanisms are considered: frictional damping of the form $CC^*u_t$ and viscoelastic damping with memory. Under suitable assumptions, we prove global well-posedness and exponential decay of solutions for sufficiently small initial data. This result is of considerable importance, as it provides a unified framework for the analysis of a wide class of neutral systems arising in structural mechanics, seismic isolation, and control theory. The abstract results are illustrated by some concrete examples. The analysis relies on a combination of semigroup theory, energy estimates, Duhamel's formula, and Gronwall-type arguments.
