State-constrained controllability of linear reaction-diffusion systems

We study the controllability of a coupled system linear parabolic equations, with nonnegativity constraint on state. establish two results to trajectories in large time: one for diagonal diffusion matrices an “approximate” constraint, and another stronger one, “exact” when all coefficients are equal eigenvalues coupling matrix have nonnegative real part. The proofs based “staircase” method. Finally, we show that state-constrained admits positive minimal time, even weaker unilateral