Decay of solutions and bilinear control to trajectories of a 1D degenerate parabolic system

This paper is concerned with the decay of solutions and the analysis of the local and global exact controllability to trajectories for a class of one-dimensional nonlinear parabolic systems with weakly degenerate diffusion coefficients. The system is controlled through the coefficient of the reaction term. Our approach relies on a well-known local inversion method combined with suitable a priori estimates specifically adapted to the degenerate setting.