  This paper addresses the problem of stabilization of $1$-D parabolic
equations with destabilizing terms and Dirichlet boundary disturbances. By
using the method of backstepping and the technique of splitting, a boundary
feedback controller is designed to ensure the input-to-state stability (ISS) of
the closed-loop system with Dirichlet boundary disturbances, while preserving
fixed-time stability (FTS) of the corresponding disturbance-free system, for
which the fixed time is either determined by the Riemann zeta function or
freely prescribed. To overcome the difficulty brought by Dirichlet boundary
disturbances, the ISS and FTS properties of the involved systems are assessed
by applying the generalized Lyapunov method. Numerical simulations are
conducted to illustrate the effectiveness of the proposed scheme of control
design.
