Pattern formation below criticality forced by noise
A stochastic partial differential equation of the Swift-Hohenberg type which is a simplified model for fluids at the convective instability is considered. The authors take a different approach that describes directly the dynamical behaviour of most realizations. The paper is organized as follows. Section 2 provides the basic notions, definitions and assumptions needed in the sequel. In addition, it contains a precise formulation of the main linear theorem which is proved in Section 3. Here the technical theorems provided by Section 4 are intensively used. The extension of the theory to nonlinear equations is discussed in Section 5 and in the last Section 6 the new wavelength estimate is derived. Everywhere in this paper the stochastic perturbation has an additive form.
stochastic partial differential equations
scientific article; zbMATH DE number 1889258