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Stability and Eigenvalue Asymptotics of Multi-Dimensional Fully Magnetic Effected Piezoelectric System with Friction-Type Infinite Memory

The long time behavior of a kind of fully magnetic effected piezoelectric system is considered. The impact of the presence of only one friction-type infinite memory term on the stability of the piezoelectric coupled plate is investigated. By introducing the so called “minimal state variable” and using semigroup theories, the system is proved to be well-posed. It is found that this kind of memory term still acts as a damping to some extent under certain conditions, but its damping effect is too weak to indirectly stabilize the system exponentially. Based on frequency domain analysis, it is further proved that this system can be indirectly stabilized polynomially by only one friction-type infinite memory term located on one of these strongly coupled PDEs. Especially, the optimality of this decay rate is also further verified by detailed spectral analysis for the system operator.

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Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.83 No.2 March-April 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 510-529

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

PIEZOELECTRIC SYSTEM WITH MAGNETIC EFFECT
POLYNOMIAL STABILITY
INFINITE MEMORY
FREQUENCY DOMAIN METHOD
OPTIMAL DECAY RATE
EIGENVALUE ASYMPTOTICS

Info Detail Spesifik

https://doi.org/10.1137/22M1486790

Pernyataan Tanggungjawab

Hai-E Zhang, Gen-Qi Xu, Zhong-Jie Han

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