带分数阶磁效应的压电梁在有/无热效应时的稳定性

Abstract

Abstract:

In this paper, we consider the well-posedness and asymptotic behavior of a one-dimensional piezoelectric beam system with control boundary conditions of fractional derivative type, which represent magnetic effects on the system. By introducing two new matrixs to deal with control boundary conditions of fractional derivative type, we obtain a new equivalent system, so as to show the well-posedness of the system by using Lumer-Philips theorem. We then prove the lack of exponential stability by a spectral analysis, and obtain the polynomial stability of the system without thermal effects by using a result of Borichev and Tomilov (Math. Ann. 347 (2010), 455-478). To find a more stable system, we then consider the stability of the above system with thermal effects described by Fourier's law, and achieve the exponential stability for the system by using the perturbed functional method.

Key words: Piezoelectric beams, Asymptotic behavior, Fractional derivative, Semigroup method

CLC Number:

O175.21

An Yanning, Liu Wenjun, Kong Aowen. Stability of Piezoelectric Beams with Magnetic Effects of Fractional Derivative Type and with/without Thermal Effects[J].Acta mathematica scientia,Series A, 2023, 43(2): 355-376.

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References

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Stability of Piezoelectric Beams with Magnetic Effects of Fractional Derivative Type and with/without Thermal Effects

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