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arXiv · 2606.20639

Uniform stabilization for relatively bounded perturbations of generators of semigroup

Shri Lal Raghudev Ram Singh·Piermarco Cannarsa·Roberto Guglielmi
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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.

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Shri Lal Raghudev Ram Singh, Piermarco Cannarsa, Roberto Guglielmi. 2026-06-02. Uniform stabilization for relatively bounded perturbations of generators of semigroup. https://arxiv.org/abs/2606.20639

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