Analyticity for Kuramoto–Sivashinsky Type Equations and Related Systems

We study the analyticity properties of solutions of Kuramoto–Sivashinsky type equations and related systems, with periodic initial data. In order to do this, we explore the sharpness of the method developed in Collet et al., 5, by investigating its applicability to other models. We prove that the solutions of a variety of dissipative-dispersive systems, which possess a global attractor, are analytic with respect to the spatial variable in a strip around the real axis; and a lower bound for the width of the strip of analyticity is obtained in each case.