Title: A Multiscale-Analysis of Stochastic Bistable Reaction-Diffusion Equations,
Abstract: A multiscale analysis of 1D stochastic bistable reaction-diffusion equations
with additive noise is carried out w.r.t. travelling waves within the
variational approach to stochastic partial differential equations. It is shown
with explicit error estimates on appropriate function spaces that up to lower
order w.r.t. the noise amplitude, the solution can be decomposed into the
orthogonal sum of a travelling wave moving with random speed and into Gaussian
fluctuations. A stochastic differential equation describing the speed of the
travelling wave and a linear stochastic partial differential equation
describing the fluctuations are derived in terms of the coefficients. Our
results extend corresponding results obtained for stochastic neural field
equations to the present class of stochastic dynamics.