The Linearized Benjamin-Bona-Mahony Equation: A Spectral Approach to Unique Continuation
نویسندگان
چکیده
This paper is devoted to analyzing a unique continuation problem for the linearized Benjamin-Bona-Mahony equation with space-dependent potentials 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 Holmgrentype 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. 2000 Mathematics Subject Classification. Primary 35B60; Secondary 47A70, 47B07.
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