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Peer-reviewedCC BY 4.0Mathematics

Stability and Energy Decay for a Porous-Elastic System with One Global Fractional Damping

  • Hualei Zhang1
  • Liao Li1
  • Shuhan Qian1
  1. 1School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China
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Abstract

In this paper, we study the stability and the energy decay for a porous-elastic system with one global fractional damping. First, by the Lumer–Phillips theorem, we show that the system is well posed. Then, by the general criteria of Arendt–Batty, we show that the system is strongly stable. Finally, by the frequency-domain method, we show that the system is polynomially stable and that the corresponding energy decay rate depends on the wave speeds μρ,δJ and the parameters α,η in the Caputo fractional derivative operator. Specifically, if μρ=δJ and η>0, the optimal energy decay rate of the system is t−21−α; if μρ≠δJ and η>0, the optimal energy decay rate of the system is t−23−α; if μρ=δJ and η=0, the energy decay rate of the system is t−2; if μρ≠δJ and η=0, the energy decay rate of the system is t−23−α.

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Cite

BibTeXRIS
BibTeX
@article{zhang2026stability,
  title = {{Stability and Energy Decay for a Porous-Elastic System with One Global Fractional Damping}},
  author = {Hualei Zhang and Liao Li and Shuhan Qian},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213919},
  url = {https://www.mdpi.com/2227-7390/14/21/3919},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Stability and Energy Decay for a Porous-Elastic System with One Global Fractional Damping
AU  - Hualei Zhang
AU  - Liao Li
AU  - Shuhan Qian
PY  - 2026
DA  - 2026/10/27
JO  - Mathematics
DO  - 10.3390/math14213919
UR  - https://www.mdpi.com/2227-7390/14/21/3919
AB  - In this paper, we study the stability and the energy decay for a porous-elastic system with one global fractional damping. First, by the Lumer–Phillips theorem, we show that the system is well posed. Then, by the general criteria of Arendt–Batty, we show that the system is strongly stable. Finally, by the frequency-domain method, we show that the system is polynomially stable and that the corresponding energy decay rate depends on the wave speeds μρ,δJ and the parameters α,η in the Caputo fractional derivative operator. Specifically, if μρ=δJ and η>0, the optimal energy decay rate of the system is t−21−α; if μρ≠δJ and η>0, the optimal energy decay rate of the system is t−23−α; if μρ=δJ and η=0, the energy decay rate of the system is t−2; if μρ≠δJ and η=0, the energy decay rate of the system is t−23−α.
SN  - 2227-7390
ER  -