Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay

Houssem Eddine Khochemane; Sara Labidi; Sami Loucif; Abdelhak Djebabla

Mathematica Bohemica (2025)

  • Issue: 1, page 109-138
  • ISSN: 0862-7959

Abstract

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We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism considered provokes an exponential decay of the solution for the case of equal speed of wave propagation. In the case of lack of exponential stability, we show that the solution decays polynomially.

How to cite

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Khochemane, Houssem Eddine, et al. "Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay." Mathematica Bohemica (2025): 109-138. <http://eudml.org/doc/299884>.

@article{Khochemane2025,
abstract = {We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism considered provokes an exponential decay of the solution for the case of equal speed of wave propagation. In the case of lack of exponential stability, we show that the solution decays polynomially.},
author = {Khochemane, Houssem Eddine, Labidi, Sara, Loucif, Sami, Djebabla, Abdelhak},
journal = {Mathematica Bohemica},
keywords = {exponential decay; polynomial decay; porous-elastic system; neutral delay; multipliers method; Faedo-Galerkin approximations},
language = {eng},
number = {1},
pages = {109-138},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay},
url = {http://eudml.org/doc/299884},
year = {2025},
}

TY - JOUR
AU - Khochemane, Houssem Eddine
AU - Labidi, Sara
AU - Loucif, Sami
AU - Djebabla, Abdelhak
TI - Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay
JO - Mathematica Bohemica
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 109
EP - 138
AB - We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism considered provokes an exponential decay of the solution for the case of equal speed of wave propagation. In the case of lack of exponential stability, we show that the solution decays polynomially.
LA - eng
KW - exponential decay; polynomial decay; porous-elastic system; neutral delay; multipliers method; Faedo-Galerkin approximations
UR - http://eudml.org/doc/299884
ER -

References

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