Abstract
We consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. By establishing an a priori estimate independent of the initial data, we show that there exists a pathwise unique, global solution to the SPDE. Furthermore, we show that the associated semi-group is Markov and possesses a unique invariant measure, supported on a Hölder–Besov space of positive regularity, which the solution law converges to exponentially fast. The a priori bound also allows us to establish tail estimates on the Lp norm of the invariant measure which are heavier than Gaussian.
Original language | English |
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Pages (from-to) | 730-772 |
Number of pages | 43 |
Journal | Stochastics and Partial Differential Equations: Analysis and Computations |
Volume | 11 |
Issue number | 2 |
Early online date | 14 Mar 2022 |
DOIs | |
Publication status | Published - 1 Jun 2023 |
Bibliographical note
Funding Information:AM gratefully acknowledges support from the EPSRC Centre For Doctoral Training in Partial Differential Equations: Analysis and Applications [grant number EP/L015811/1].
Publisher Copyright:
© 2022, The Author(s).
Keywords
- Advection-diffusion SPDE
- Chemotaxis
- Exponential ergodicity
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics