We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strateg...

In this article, we consider a non-local variant of the Kuramoto-Sivashinsky equation in three dimensions (2D interface). Besides showing global wellposedness also obtain some qualitative properties solutions. particular, prove that solutions become analytic spatial variable for positive time, existence compact attractor and an upper bound on number oscillations We observe such is particularly ...