Second-Kind Equilibrium States of the Kuramoto–Sivashinsky Equation with Homogeneous Neumann Boundary Conditions

摘要

Abstract In this paper, we consider the boundary-value problem for the Kuramoto–Sivashinsky equation with homogeneous Neumann conditions. The problem on the existence and stability of second-kind equilibrium states was studied in two ways: by the Galerkin method and by methods of the modern theory of infinite-dimensional dynamical systems. Some differences in results obtained are indicated.