Stabilisation by noise on the boundary for a Chafee-Infante equation with dynamical boundary conditions
Analysis of PDEs
2018-11-14 v2 Optimization and Control
Abstract
The stabilisation by noise on the boundary of the Chafee-Infante equation with dynamical boundary conditions subject to a multiplicative It\^o noise is studied. In particular, we show that there exists a finite range of noise intensities that imply the exponential stability of the trivial steady state. This differs from previous works on the stabilisation by noise of parabolic PDEs, where the noise acts inside the domain and stabilisation typically occurs for an infinite range of noise intensities. To the best of our knowledge, this is the first result on the stabilisation of PDEs by boundary noise.
Keywords
Cite
@article{arxiv.1803.11058,
title = {Stabilisation by noise on the boundary for a Chafee-Infante equation with dynamical boundary conditions},
author = {Klemens Fellner and Stefanie Sonner and Bao Quoc Tang and Do Duc Thuan},
journal= {arXiv preprint arXiv:1803.11058},
year = {2018}
}
Comments
to appear in Discrete and Continuous Dynamical Systems - Series B