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Exact controllability of the wave equation with time-dependent and variable coefficients
Institution:1. Institut de Mathématiques de Bordeaux, Université de Bordeaux, Bordeaux, France;2. São Paulo State University (UNESP), Institute of Biosciences, Department of Biostatistics, Botucatu, Brazil;1. Academy of Romanian Scientists, Splaiul Independen?ei 54, 050094 Bucharest, Romania;2. Faculty of Mathematics and Computer Science, Babe?-Bolyai University, 1 M. Kog?lniceanu Str., 400084 Cluj-Napoca, Romania;3. Department of Applied Mathematics, University of Craiova, 13 A.I. Cuza Str., 200585 Craiova, Romania;1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;2. College of Science, Henan University of Technology, Zhengzhou 450001, China;3. Henan Key Laboratory of Financial Engineering, Zhengzhou 450001, China
Abstract:This paper deals with boundary exact controllability for the dynamics governed by the wave equation with variable coefficients in time and space, subject to Dirichlet or Neumann boundary controls. The observability inequalities are established by the Riemannian geometry method under some geometric conditions.
Keywords:Wave equation with variable coefficients  Exact controllability  Riemannian manifold
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