Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equation under the Bardos-Lebeau-Rauch geometric control condition

✍ Scribed by K.-D. Phung

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 488 KB
• Volume: 44
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(02)00256-0

✦ Synopsis

We extend the result of the null controllability property of the heat equation, obtained as limit, when e tends to zero, of the exact controllability of a singularly perturbed damped wave equation depending on a parameter e > 0, described in [1], to bounded domains which satisfy the Bardos-Lebeau-Rauch geometric control condition [2]. We add to the method of Lopez, Zhang and Zuazua in [1] an explicit in e > 0 observability estimate for the singularly perturbed damped wave equation under the Bardos-Lebeau-Rauch geometric control condition. Here the geometric conditions axe more optimal than in [1] and the proof is simpler than in [1]. Instead of using global Carleman inequalities as in [1], we apply an integral representation formula. (~