Stabilization of the heat equation with disturbance at the flux boundary condition

In this paper, we address the problem of boundary stabilization heat equation subjected to an unknown disturbance, which is assumed be acting at flux condition. By means Lyapunov techniques and use sign multivalued operator, responsible rejecting effects design a feedback law obtain exponential stability closed-loop system. The well-posedness system, differential inclusion, shown with maximal monotone operator theory.