Prescribed-time stabilisation for uncertain reaction-diffusion equations with Neumann boundary control

We study the Neumann boundary feedback stabilisation for reaction-diffusion equations with matched boundary uncertainties (including internal uncertainty and external disturbance) within a prescribed time, where the convergence time is independent of initial conditions and can be prescribed a priori. We first estimate the uncertainties within the prescribed time by constructing an estimator and then propose the prescribed-time boundary control law by utilising backstepping transformation with a time-varying kernel. Neumann boundary control is verified to be uniformly bounded.