A Stochastic Model of Chemorepulsion with Additive Noise and Nonlinear Sensitivity

Ilya Chevyrev, Ben Hambly, Avi Mayorcas

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. We show that for any suitable initial data 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. We also establish tail bounds on the invariant measure that are heavier than Gaussian when measured using any Lp norm.
Original languageEnglish
Number of pages31
JournalStochastics and Partial Differential Equations: Analysis and Computations
Publication statusAccepted/In press - 14 Feb 2022

Fingerprint

Dive into the research topics of 'A Stochastic Model of Chemorepulsion with Additive Noise and Nonlinear Sensitivity'. Together they form a unique fingerprint.

Cite this