Blumenthal, Alex and Engel, Maximilian and Neamţu, Alexandra
(2023)
*On the pitchfork bifurcation for the Chafee-Infante equation with additive noise.*
Probability Theory and Related Fields, 187
.
pp. 603-627.

Full text not available from this repository.

Official URL: https://doi.org/10.1007/s00440-023-01235-3

## Abstract

We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor is a singleton, independently of the value of the bifurcation parameter; this phenomenon is often referred to as the “destruction” of the bifurcation by the noise. Analogous to the results of Callaway et al. (AIHP Prob Stat 53:1548–1574, 2017) for a 1D stochastic ODE, we show that some remnant of the bifurcation persists for this SPDE model in the form of a positive finite-time Lyapunov exponent. Additionally, we prove finite-time expansion of volume with increasing dimension as the bifurcation parameter crosses further eigenvalues of the Laplacian.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3065 |

Deposited By: | Jana Jerosch |

Deposited On: | 05 Feb 2024 12:55 |

Last Modified: | 05 Feb 2024 12:55 |

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