The impact of white noise on a supercritical bifurcation in the Swift-Hohenberg equation

DOI10.1016/j.physd.2020.132742zbMath1483.60088arXiv2005.09676OpenAlexW3091154086MaRDI QIDQ2116295

Luigi Amedeo Bianchi, Dirk Blömker

Publication date: 16 March 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.09676

zbMATH Keywords

averagingsupercritical bifurcationmodulation equationamplitude equationSwift-Hohenbergimpact of noise

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Pattern formations in context of PDEs (35B36)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modulation equation for SPDEs in unbounded domains with space-time white noise -- linear theory
• Stochastic maximal \(L^{p}\)-regularity
• Maximal regularity for stochastic convolutions in \(L^p\) spaces
• Multiscale expansion of invariant measures for SPDEs
• Stochastic evolution equations with a spatially homogeneous Wiener process
• Amplitude equation for the generalized Swift-Hohenberg equation with noise
• Modulation equation and SPDEs on unbounded domains
• Synchronization by noise
• Restricted Markov uniqueness for the stochastic quantization of \(P(\Phi)_{2}\) and its applications
• Global well-posedness of the dynamic \(\Phi^{4}\) model in the plane
• Amplitude modulation for the Swift-Hohenberg and Kuramoto-Sivashinski equations
• Additive noise destroys the random attractor close to bifurcation
• ASYMPTOTIC COMPACTNESS OF STOCHASTIC COMPLEX GINZBURG–LANDAU EQUATION ON AN UNBOUNDED DOMAIN
• The validity of modulation equations for extended systems with cubic nonlinearities
• Nonlinear PDEs
• Modulation Equation for Stochastic Swift--Hohenberg Equation
• <scp>Space‐Time</scp> Localisation for the Dynamic Model
• Pattern formation outside of equilibrium
• Localized States in an Extended Swift–Hohenberg Equation