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Unique Continuation for the Linearized Benjamin-Bona-Mahony Equation with Space-Dependent Potential

Zhang, Xu and Zuazua Iriondo, Enrique (2003) Unique Continuation for the Linearized Benjamin-Bona-Mahony Equation with Space-Dependent Potential. Mathematische Annalen, 326 (3). 543-582 . ISSN 0025-5831

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Abstract

In this paper, we analyze the unique continuation problem for the linearized Benjamin-Bona-Mahony equation with space-dependent potential in a bounded interval with Dirichlet boundary conditions. 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.

Item Type:Article
Uncontrolled Keywords:Energy Decays, Stabilization
Subjects:Sciences > Mathematics > Differential equations
ID Code:12299
Deposited On:01 Mar 2011 09:28
Last Modified:06 Jun 2011 09:35

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