Stabilization of linear heat equation with a heat source at intermediate point by boundary control

In this paper, the stabilization of a linear heat equation with a heat source at intermediate point is discussed applying the backstepping method. Firstly, we prove the existence of kernels in the forward and inverse transformation by some special techniques; secondly, we obtain the exponential stability with any prescribed decay rate of a closed-loop system; finally, the effectiveness of the explicit feedback stabilization controller design is illustrated with some numerical examples.