Exact controllability for the nonlinear Burgers-KdV equation

Using the Leray-Schauder fixed point theorem and the theory of dissipative operators, we first consider the solution of the linear Burgers-KdV equation. Second we find the control function h by using some inequalities, the theory of monotone operators and division integral theory. Finally we prove the exact controllability for the Burgers-KdV equation, that is to say, for suitable T > 0, for any given initial state u⁰ ∈ H^S and terminal state u^T ∈ H^S, we can find an appropriate control function h which drives the solution u for Burgers-KdV equation to satisfy u (x, 0) = u⁰ and u (x, T) = u^T.