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• W3201311893 abstract "In this paper, we consider a dissipative system of one-dimensional piezoelectric beam with magnetic effect and a tip load at the free end of the beam, which is modeled as a special form of double boundary dissipation. Our main aim is to study the well-posedness and asymptotic behavior of this system. By introducing two functions defined on the right boundary, we first transform the original problem into a new abstract form, so as to show the well-posedness of the system by using Lumer-Philips theorem. We then divide the original system into a conservative system and an auxiliary system, and show that the auxiliary problem generates a compact operator. With the help of Wely's theorem, we obtain that the system is not exponentially stable. Moreover, we prove the polynomial stability of the system by using a result of Borichev and Tomilov (Math. Ann. {bf 347} (2010), 455--478)." @default.
• W3201311893 created "2021-09-27" @default.
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• W3201311893 date "2021-09-20" @default.
• W3201311893 modified "2023-09-25" @default.
• W3201311893 title "Polynomial stability of piezoelectric beams with magnetic effect and tip body" @default.
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• W3201311893 doi "https://doi.org/10.48550/arxiv.2109.09469" @default.
• W3201311893 hasPublicationYear "2021" @default.
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