
























Abstract:In this paper, we study the robustness of exponential stability for semigroups generated by linear operators under perturbations. Extending a classical result of Gibson's Stability Theorem, we show that if the generator of an analytic exponentially stable semigroup is perturbed by a class of relatively bounded operators satisfying certain assumptions, then exponential stability is preserved, provided the perturbed semigroup is strongly stable. We also show that, for a restricted class of perturbations, the analyticity requirement can be relaxed to Gevrey regularity. Moreover, we present applications to uniformly parabolic equations, degenerate/singular parabolic equations, coupled hyperbolic plate systems, and generalized coupled systems of Kirchhoff-Love plates and a membrane-like electric network.
From: Shri Lal Raghudev Ram Singh [view email]
[v1]
Tue, 2 Jun 2026 14:56:31 UTC (39 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。