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, t<inf>1</inf>] if and only if the following algebraic condition holds Rank[B<inf>j</inf>] = γ<inf>j</inf>, where B<inf>j</inf> acts from ℝ^m to R(E<inf>j</inf>), λ<inf>j</inf>'s are the eigenvalues of -Δ with Dirichlet boundary condition and λ<inf>j</inf> the corresponding multiplicity, E<inf>j</inf>'s are the projections on the corresponding eigenspace and R(E<inf>j</inf>) denotes the range of E<inf>j</inf>.

Año de publicación:

2008

Keywords:

• Approximate controllability
• BBM- Equation
• Algebraic condition

Fuente:

scopus

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