Adames, N.; Leiva, H.; Sánchez, J. Controllability of the Benjamin-Bona-Mahony equation. (English) Zbl 1217.93027 Divulg. Mat. 16, No. 1, 29-37 (2008). Summary: 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 \([0, t_1]\) if and only if the following algebraic condition holds: \(\mathrm{Rank} B_j = \gamma_j\) , where \(B_j\) maps from \(\mathbb{R}^m\) to \(R(E_j)\), \(\lambda_j\)’s are the eigenvalues of \(-\Delta\) with Dirichlet boundary condition and \(\gamma j\) the corresponding multiplicity, \(E_j\)’s are the projections on the corresponding eigenspace and \(R(E_j)\) denotes the range of \(E_j\). MSC: 93B05 Controllability 35B41 Attractors 35Q53 KdV equations (Korteweg-de Vries equations) 93C20 Control/observation systems governed by partial differential equations Keywords:BBM-equation; algebraic condition; approximate controllability PDFBibTeX XMLCite \textit{N. Adames} et al., Divulg. Mat. 16, No. 1, 29--37 (2008; Zbl 1217.93027) Full Text: EuDML EMIS