Null controllability of a coupled nonlinear parabolic system

This paper deals with the null controllability of a coupled nonlinear parabolic system. The coefficients of the system operators depend on the states, and the control acts through the first equation. To solve the control problem of the linearized system, we use maximum regularity results in the spaces $L^q(0,T,L^p(\mathrm{\Omega }))$, and we use Liusternick's inverse function theorem for the nonlinear controllability problem. In addition, as an appendix, we prove the well-posedness of the system.