Unique continuation for the linearized Benjamin-Bona-Mahony equation with space-dependent potential (Q1566353)

A unique continuation problem for the linearized Benjamin-Bona-Mahony equation with space-dependent potential is analysed in a bounded interval with Dirichlet boundary conditions. The underlying Cauchy problem is a characteristic one. Two unique condition results by means of spectral analysis and the generalized eigenvector expansion of the solution are proved. It is found that the unique continuation property depends very strongly on the nature of the potential and not only on its boundedness or integrability properties.