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Optimal damping design and exponential stabilization for weakly degenerate wave equations
Abstract
We investigate the optimal damping design and exponential stabilization for a class of higher-dimensional weakly degenerate damped wave equations. In weighted Sobolev spaces, we establish well-posedness and uniform exponential energy decay, and verify the existence of long-time optimal damping potentials. To overcome analytical difficulties arising from system non-self-adjointness, we use finite-time approximation via semigroup operator norms. Through linearization and adjoint-state analysis, we derive first-order necessary optimality conditions and show finite-time optimal dampings possess a bang-bang structure.
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BibTeX
@misc{gu2026optimal,
title = {{Optimal damping design and exponential stabilization for weakly degenerate wave equations}},
author = {Mengze Gu and Dong-Hui Yang and Hongli Sun and Yuanzhi Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27502},
eprint = {2609.27502},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27502},
}
RIS
TY - UNPB
TI - Optimal damping design and exponential stabilization for weakly degenerate wave equations
AU - Mengze Gu
AU - Dong-Hui Yang
AU - Hongli Sun
AU - Yuanzhi Zhou
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27502
UR - https://arxiv.org/abs/2609.27502
AB - We investigate the optimal damping design and exponential stabilization for a class of higher-dimensional weakly degenerate damped wave equations. In weighted Sobolev spaces, we establish well-posedness and uniform exponential energy decay, and verify the existence of long-time optimal damping potentials. To overcome analytical difficulties arising from system non-self-adjointness, we use finite-time approximation via semigroup operator norms. Through linearization and adjoint-state analysis, we derive first-order necessary optimality conditions and show finite-time optimal dampings possess a bang-bang structure.
ER -