201. Polynomial stability of piezoelectric beams with magnetic effect and tip body.
- Author
-
Yanning An, Wenjun Liu, and Aowen Kong
- Subjects
COMPACT operators ,POLYNOMIALS - 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–Phillips 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 Weyl’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. 347 (2010), 455–478). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF