Peer-reviewedCC BY 4.0Axioms
Energy Decay Rate for a Porous-Elastic System with Fractional Infinite Memory
- 1School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China
Abstract
In this paper, we study the energy decay rate for a porous-elastic system with fractional infinite memory, which acts on the material displacement equation. Using the frequency domain method, we show that the energy decay rate of the system depends on the order θ of the fractional operator and the wave speeds μρ and δJ, where θ∈[0,1]. Specifically, the energy of the system decays exponentially when θ=1 and μρ=δJ. The energy of the system decays polynomially when θ∈[0,1) and μρ=δJ or θ∈[0,1] and μρ≠δJ. In addition, we also show that the polynomial decay rates obtained are optimal in some sense.
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BibTeX
@article{zhang2026energy,
title = {{Energy Decay Rate for a Porous-Elastic System with Fractional Infinite Memory}},
author = {Hualei Zhang},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100770},
url = {https://www.mdpi.com/2075-1680/15/10/770},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Energy Decay Rate for a Porous-Elastic System with Fractional Infinite Memory
AU - Hualei Zhang
PY - 2026
DA - 2026/10/14
JO - Axioms
DO - 10.3390/axioms15100770
UR - https://www.mdpi.com/2075-1680/15/10/770
AB - In this paper, we study the energy decay rate for a porous-elastic system with fractional infinite memory, which acts on the material displacement equation. Using the frequency domain method, we show that the energy decay rate of the system depends on the order θ of the fractional operator and the wave speeds μρ and δJ, where θ∈[0,1]. Specifically, the energy of the system decays exponentially when θ=1 and μρ=δJ. The energy of the system decays polynomially when θ∈[0,1) and μρ=δJ or θ∈[0,1] and μρ≠δJ. In addition, we also show that the polynomial decay rates obtained are optimal in some sense.
SN - 2075-1680
ER -