A stochastic model of chemorepulsion with additive noise and nonlinear sensitivity

Abstract We consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. By establishing an priori estimate independent of initial data, we show that there exists pathwise unique, global solution to SPDE. Furthermore, associated semi-group is Markov and possesses unique invariant measure, supported Hölder–Besov space positive regularity, which law converges exponentially fast. The bound also allows us establish tail estimates $$L^p$$ Lp norm measure are heavier than Gaussian.