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Controllability of the benjamin-bona-mahony equation

Abstract:

In this note we study the controllability of the Generalized Benjamin-Bona-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 ℝm to R(Ej), λj's are the eigenvalues of -Δ with Dirichlet boundary condition and λj the corresponding multiplicity, Ej's are the projections on the corresponding eigenspace and R(Ej) denotes the range of Ej.