Controllability of the Benjamin-Bona-Mahony Equation Controlabilidad de la Ecuación de Benjamin-Bona-Mahony
نویسندگان
چکیده
Abstract In this note we study the controllability of the Generalized BenjaminBona-Mahony equation (BBM) with homogeneous Dirichlet boundary conditions. Under some conditions we shall prove the system is approximately controllable on [0, t1] if and only if the following algebraic condition holds Rank[Bj ] = γj , where Bj acts from IR m to R(Ej), λj ’ s are the eigenvalues of −∆ with Dirichlet boundary condition and γj the corresponding multiplicity, Ej ’s are the projections on the corresponding eigenspace and R(Ej) denotes the range of Ej .
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