Local stabilization of coupled nonlinear parabolic equations by boundary control

This paper considers local stabilization of a boundary control system coupled by nonlinear parabolic equations. Based on backstepping approach, a linear Volterra-type integral transformation maps the system into another homogeneous target system, and an explicit feedback control law is obtained. Local exponential stabilization of the closed loop is established. A system with three coupled nonlinear parabolic equations is simulated, which show that the obtained feedback control law is feasible.