Work

Optimal damping design and exponential stabilization for weakly degenerate wave equations

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.27502

Authors: Gu, Mengze, Yang, Dong-Hui, Sun, Hongli, Zhou, Yuanzhi

Institutions: Changsha Normal University, Central South University, Chongqing University of Science and Technology

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214156992

Cites: 2

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Related to: 10