Null controllability of a coupled system of degenerate parabolic equations with lower order terms
Texas State University, Department of Mathematics
This article concerns the null controllability of a control system governed by coupled degenerate parabolic equations with lower order terms. For these equations, the convection terms cannot be controlled by the diffusion terms. We establish a Carleman estimate and an observability inequality by using Carleman estimates for single degenerate parabolic equations with lower order term and some energy estimates. Then we prove that the system with two controls is null controllable. Finally, we show the null controllability of the system with one control, by constructing suitable controls.
Carleman estimate, Null controllability, Coupled degenerate equations, Convection terms
Xu, J., Zhou, Q., & Nie, Y. (2019). Null controllability of a coupled system of degenerate parabolic equations with lower order terms. <i>Electronic Journal of Differential Equations, 2019</i>(103), pp. 1-12.