Stabilization of Series Heat Equations with One Boundary Control

In this paper, we consider the exponential stabilization for a series system of N heat equations, where one boundary control is only applied to the leading (first) heat equation, and the boundary temperature of the previous heat is fed into the boundary heat flux of the next one. With N invertible transformations, we present a boundary feedback control so that the closed-loop system is equivalent to an exponentially stable target system. Some numerical simulation results are presented to validate the theoretical conclusions.