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arXiv · 2603.27525

A Class of Degenerate Hyperbolic Equations with Neumann Boundary Conditions and Its Application to Observability

Dong-Hui Yang·Jie Zhong
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Abstract

We establish a mixed observability inequality for a class of degenerate hyperbolic equations on the cylindrical domain $\Omega = \mathbb{T} \times (0,1)$ with mixed Neumann Dirichlet boundary conditions. The degeneracy acts only in the radial variable, whereas the periodic angular variable allows propagation with a strong tangential component, making a direct top boundary observation delicate. For $\alpha \in [1,2)$, we prove that the solution can be controlled by a boundary observation on the top boundary together with an interior observation on a narrow strip. The proof combines a weighted functional framework, improved regularity, a cutoff decomposition in the angular variable, a multiplier argument for the localized component, and an energy estimate for the remainder.

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Dong-Hui Yang, Jie Zhong. 2026-03-29. A Class of Degenerate Hyperbolic Equations with Neumann Boundary Conditions and Its Application to Observability. https://arxiv.org/abs/2603.27525

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