{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:36:08Z","timestamp":1787322968971,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>For the linear wave equation with time-invariant coefficients on a connected compact Riemannian manifold $(\\Omega,g)$ with $C^{3}$ boundary, the geodesics condition of Bardos, Lebeau, and Rauch [SIAM J. Control Optim., 30 (1992), pp. 1024--1065] is characterized in terms of escape functions, which are some Lyapunov functions on the phase space $S^{*}\\bar{\\Omega}$ (the unit sphere cotangent bundle). Differentiable escape functions yield a sufficient condition which is slightly less sharp but does not refer to geodesics. The escape function condition yields a straightforward geometric proof that the geodesics condition holds in the situations where first order differential multiplier methods apply. Using microlocal control results, it allows us to generalize some control results (that were obtained by multiplier methods) to variable coefficients and lower order terms. It also allows us to prove, in some class of simple situations (e.g., in $\\mathbb{R}^{2}$ with constant coefficients), that no first order differential multiplier method can reach the optimal control time or control regions.<\/jats:p>","DOI":"10.1137\/s036301290139107x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1554-1566","source":"Crossref","is-referenced-by-count":40,"title":["Escape Function Conditions for the Observation, Control, and Stabilization of the Wave Equation"],"prefix":"10.1137","volume":"41","author":[{"given":"Luc","family":"Miller","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01877510"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0330055"},{"key":"R3","first-page":"126","author":"Burq Nicolas","year":"1993","journal-title":"M\u00e9m. 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