2021
DOI: 10.48550/arxiv.2109.09739
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Stability of piezoelectric beams with magnetic effects of fractional derivative type and with/without thermal effects

Abstract: In this paper, we first consider the well-posedness and asymptotic behavior of a onedimensional piezoelectric beam system with control boundary conditions of fractional derivative type, which represent magnetic effects on the system. By introducing two new equations 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 … Show more

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