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The stabilisation by noise on the boundary of the Chafee-Infante equationwith dynamical boundary conditions subject to a multiplicative It\^o noise isstudied. In particular, we show that there exists a finite range of noiseintensities that imply the exponential stability of the trivial steady state.This differs from previous works on the stabilisation by noise of parabolicPDEs, where the noise acts inside the domain and stabilisation typically occursfor an infinite range of noise intensities. To the best of our knowledge, thisis the first result on the stabilisation of PDEs by boundary noise.

Stabilisation by noise on the boundary for a Chafee-Infante equation with dynamical boundary conditions