Abstract
In this paper, we analyze a unique continuation problem for the linearized Benjamin-Bona-Mahony equation with space-dependent potential in a bounded interval with Dirichlet boundary conditions. The underlying Cauchy problem is a characteristic one. We prove two unique continuation results by means of spectral analysis and the (generalized) eigenvector expansion of the solution, instead of the usual Holmgren-type method or Carleman-type estimates. It is found that the unique continuation property depends very strongly on the nature of the potential and, in particular, on its zero set, and not only on its boundedness or integrability properties.
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Received: 6 December 2001 / Revised version: 13 June 2002 / Published online: 10 February 2003
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ID="⋆" Supported by a Postdoctoral Fellowship of the Spanish Education and Culture Ministry, the Foundation for the Author of National Excellent Doctoral Dissertation of P.R. China (Project No: 200119), and the NSF of China under Grant 19901024
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ID="⋆⋆" Supported by grant PB96-0663 of the DGES (Spain) and the EU TMR Project "Homogenization and Multiple Scales".
Mathematics Subject Classification (2000): 35B60, 47A70, 47B07
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Zhang, X., Zuazua, E. Unique continuation for the linearized Benjamin-Bona-Mahony equation with space-dependent potential. Math. Ann. 325, 543–582 (2003). https://doi.org/10.1007/s00208-002-0391-8
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DOI: https://doi.org/10.1007/s00208-002-0391-8