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arXiv · 2609.27502

Optimal damping design and exponential stabilization for weakly degenerate wave equations

Mengze Gu·Dong-Hui Yang·Hongli Sun·Yuanzhi Zhou
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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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Mengze Gu, Dong-Hui Yang, Hongli Sun, Yuanzhi Zhou. 2026-09-23. Optimal damping design and exponential stabilization for weakly degenerate wave equations. https://arxiv.org/abs/2609.27502

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