{"ID":6537416,"CreatedAt":"2026-07-14T02:54:43.516908796Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.11702","arxiv_id":"2607.11702","title":"Uniform controllability for the wave equation with large potential","abstract":"This paper investigates the dependence of the control cost for a wave equation with respect to perturbation by a time-independent potential $\\lmbd V$ scaled by a large parameter $\\lmbd$ on a compact Riemannian manifold. We introduce the geometric control condition~\\eqref{GCC+}, a variant of the geometric control condition of Bardos--Lebeau--Rauch--Taylor, tailored to accommodate the influence of the potential $V$. We show that~\\eqref{GCC+} is necessary and sufficient for the existence of a uniform \\emph{observability cost} with respect to the large parameter $\\lmbd$. We provide geometric examples satisfying~\\eqref{GCC+} and estimate the blow-up rate of the \\emph{observability cost} in situations where it fails. The proofs rely on semiclassical and second microlocal defect measures.","short_abstract":"This paper investigates the dependence of the control cost for a wave equation with respect to perturbation by a time-independent potential $\\lmbd V$ scaled by a large parameter $\\lmbd$ on a compact Riemannian manifold. We introduce the geometric control condition~\\eqref{GCC+}, a variant of the geometric control condit...","url_abs":"https://arxiv.org/abs/2607.11702","url_pdf":"https://arxiv.org/pdf/2607.11702v1","authors":"[\"Arthur Yax\"]","published":"2026-07-13T15:33:35Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}