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

2018/03/29 by Klemens Fellner, Fellner, Klemens, Stefanie Sonner +5 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1803.11058

openalex publication_date 2018/03/29 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

The stabilisation by noise on the boundary of the Chafee-Infante equation\nwith dynamical boundary conditions subject to a multiplicative It ^o noise is\nstudied. In particular, we show that there exists a finite range of noise\nintensities that imply the exponential stability of the trivial steady state.\nThis differs from previous works on the stabilisation by noise of parabolic\nPDEs, where the noise acts inside the domain and stabilisation typically occurs\nfor an infinite range of noise intensities. To the best of our knowledge, this\nis the first result on the stabilisation of PDEs by boundary noise.\n

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