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arXiv · 2609.06049

Stability of Magnetizable Piezoelectric Beam Systems with Two Fractional Infinite Memory Terms

Jun Zhou·Linfeng Duan
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Abstract

In this paper, we investigate a class of magnetizable piezoelectric beam systems with two fractional infinite memory terms, whose fractional orders are denoted by \(\theta_1, \theta_2 \in [0,1]\). By introducing the Dafermos history variable, we construct an augmented state space and reformulate the system as an abstract evolution equation. The well-posedness of the system is established via semigroup theory. Through a frequency-domain analysis, we characterize the asymptotic behavior of the solutions. We show that the system is exponentially stable if \(\theta_1 = \theta_2 = 1\), and is polynomially stable in all other cases, with the explicit decay rate \(t^{-\frac{1}{2-2\theta_0}}\), where \(\theta_0 = \min\{\theta_1, \theta_2\}\). Furthermore, the optimality of the obtained decay rate is verified.

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Jun Zhou, Linfeng Duan. 2026-09-05. Stability of Magnetizable Piezoelectric Beam Systems with Two Fractional Infinite Memory Terms. https://arxiv.org/abs/2609.06049

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