Stabilization of three-heat cascade system with one boundary control

In this paper, we consider the exponential stabilization for a cascade system of three heat equations, where one boundary control is only applied to the first heat equation and the point output of the heat is flowing into the next one. By three invertible transformations, the heat system is converted into an exponentially stable target system, and we present a boundary feedback control. The numerical simulations are presented to illustrate the effect of the stabilizing controller.