Explicit observation of Schrödinger equation with potential

Article type: Research Article

Authors: Maddouri, Feten

Affiliations: Ecole National d'ingénieur de Tunis, Laboratoire LAMSIN, B.P. 37, 1002 Tunis, Tunisie. E-mail: feten.maddouri@lamsin.rnu.tn

Note: [] Supported by the Tunisian Ministry for Scientific Research and Technology (MRST), within the LAB-STI-02 program.

Abstract: We study an explicit interior observability estimate for the Schrödinger equation with potential in a bounded domain of RN (N≥1), and with zero Dirichlet boundary condition. The method combines Carleman inequality and multiplier techniques. Moreover, by microlocal analysis tools, we prove a precised observability estimate in high frequencies.

Keywords: Schrödinger equation, observability estimate, Carleman inequality, microlocal analysis

DOI: 10.3233/ASY-2009-0947

Journal: Asymptotic Analysis, vol. 65, no. 1-2, pp. 59-78, 2009