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<p>In this work, we study the exponential stability of a piezoelectric beam subjected to magnetic effects and dissipation via microtemperatures. The model is formulated as a system of coupled partial differential equations, including a thermal equation to capture the dissipative effects at a microscopic scale. First, we establish the well-posedness of the problem within the framework of semigroup theory. Then, we use the energy method to derive sufficient conditions for the exponential stability of the system. Additionally, we conduct numerical experiments using finite differences to validate the theoretical results. Our findings indicate that the inclusion of dissipation due to microtemperatures plays a significant role in stabilizing the system, reducing undesired oscillations, and improving the energy decay rate.</p>

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Mathematical and Numerical Investigation of the Exponential Stability of Piezoelectric Beams Under Magnetic and Microtemperature Effects

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Carlos A. S. Nonato,
  • Vinicius S. Paula,
  • Jorge A. J. Avila,
  • Flávio A. F. Nascimento

摘要

In this work, we study the exponential stability of a piezoelectric beam subjected to magnetic effects and dissipation via microtemperatures. The model is formulated as a system of coupled partial differential equations, including a thermal equation to capture the dissipative effects at a microscopic scale. First, we establish the well-posedness of the problem within the framework of semigroup theory. Then, we use the energy method to derive sufficient conditions for the exponential stability of the system. Additionally, we conduct numerical experiments using finite differences to validate the theoretical results. Our findings indicate that the inclusion of dissipation due to microtemperatures plays a significant role in stabilizing the system, reducing undesired oscillations, and improving the energy decay rate.