Abstract
AbstractWe 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$$L^p$$Lpnorm of the invariant measure which are heavier than Gaussian.
Funder
engineering and physical sciences research council
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Modeling and Simulation,Statistics and Probability
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