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. 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 languageEnglish
Pages (from-to)730-772
Number of pages43
JournalStochastics and Partial Differential Equations: Analysis and Computations
Volume11
Issue number2
Early online date14 Mar 2022
DOIs
Publication statusPublished - 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

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