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

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 so...

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Bibliographic Details
Main Authors: Houssem Eddine Khochemane, Sara Labidi, Sami Loucif, Abdelhak Djebabla
Format: Article
Language:English
Published: Institute of Mathematics of the Czech Academy of Science 2025-04-01
Series:Mathematica Bohemica
Subjects:
Online Access:https://mb.math.cas.cz/full/150/1/mb150_1_7.pdf
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Summary: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.
ISSN:0862-7959
2464-7136