PreprintCC BY-NC-ND 4.0HAL
Note on the Exponential Stability of the Viscoelastic Wave Equation
Abstract
In this article, we study the viscoelastic wave equation with a localized history memory term, and without frictional damping. Under the geometric control condition on the memory region, we prove exponential decay of the viscoelastic energy using the Gearhart-Prüss-Huang Theorem. We prove in high frequency that a loss of derivative is compensated by a decay in frequency.
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BibTeX
@misc{gagnon2026note,
title = {{Note on the Exponential Stability of the Viscoelastic Wave Equation}},
author = {Ludovick Gagnon},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06281},
eprint = {2610.06281},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05773554v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Note on the Exponential Stability of the Viscoelastic Wave Equation
AU - Ludovick Gagnon
PY - 2026
DA - 2026/10/01
PB - HAL
DO - 10.48550/arxiv.2610.06281
UR - https://hal.science/hal-05773554v1
AB - In this article, we study the viscoelastic wave equation with a localized history memory term, and without frictional damping. Under the geometric control condition on the memory region, we prove exponential decay of the viscoelastic energy using the Gearhart-Prüss-Huang Theorem. We prove in high frequency that a loss of derivative is compensated by a decay in frequency.
ER -