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

  • * Corresponding author: Stefanie Sonner

    * Corresponding author: Stefanie Sonner 

Our research was supported by the ASEAN-European Academic University Network (ASEA-UNINET), and partially supported by NAWI Graz, IGDK 1754, and NAFOSTED project 101.01-2017.302

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  • The stabilisation by noise on the boundary of the Chafee-Infante equation with dynamical boundary conditions subject to a multiplicative Itô 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.

    Mathematics Subject Classification: Primary: 34H15, 35K57; Secondary: 35P15, 35R60.


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